Publications
Research publications of the LIMO Lab in reverse chronological order.
Search LIMO publications by title, author, or venue, then narrow the results by research topic. “Highlighted only” is an editorial selection maintained by the website team and can be combined with the other filters.
2026
- Preprint
Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors
arXiv preprint arXiv:2609.33897, Sep 2026Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis–Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka–Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson–Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.
@article{qin2026mixednoise, title = {Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors}, author = {Qin, Ziqi and Tan, Hong Ye and Biguri, Ander and Liang, Jingwei and Schönlieb, Carola-Bibiane}, journal = {arXiv preprint arXiv:2609.33897}, year = {2026}, month = sep, } - Preprint
Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions
arXiv preprint arXiv:2609.13010, Sep 2026Optimal transport (OT) compares distributions and aligns datasets in machine learning, yet unregularized discrete OT requires a linear program with quadratically many transport variables. We propose HELLO, a hierarchical solver that casts large-scale discrete OT as edge localization and uses dual potentials to guide both coarse-to-fine initialization and within-level refinement. Initialization propagates coarse dual potentials across a recursive subsampling hierarchy to assign candidate edges. Refinement then iteratively inserts the largest dual violators in each row and column until the relative KKT residual meets a prescribed tolerance, while budgeted pruning ensures linear memory complexity. For exact-arithmetic refinement, we prove finite termination at a global optimum under a symbolic lexicographic rule. At the million-point scale, HELLO attains lower transport objectives with order-of-magnitude runtime improvements over strong baselines across feature dimensions from single digits to thousands. It further scales to 1.28 million samples per marginal in 8192 dimensions on a single H100, using 41.6 GiB peak GPU memory while satisfying a full relative KKT residual below 10^-6. Beyond standard discrete OT, the framework supports general pairwise costs and serves as a scalable balanced-OT oracle for semi-discrete OT, Gromov–Wasserstein, unbalanced OT, and OT-based Flow Matching.
@article{xia2026dualguided, title = {Dual-guided Hierarchical Edge Localization for Large-scale Optimal Transport Across Dimensions}, author = {Xia, Wenzhou and Ding, Qiaoqiao and Liang, Jingwei and Zhang, Xiaoqun}, journal = {arXiv preprint arXiv:2609.13010}, year = {2026}, month = sep, } - Preprint
GMTS: Gradient Magnitude-based Token Selection Improves RLVR Training for LLM Reasoning
arXiv preprint arXiv:2608.30632, Aug 2026Reinforcement learning (RL), particularly RL with Verifiable Rewards (RLVR), has recently emerged as a central paradigm for enhancing large language models’ (LLMs) reasoning abilities, demonstrating remarkable effectiveness across reasoning tasks. Recent studies suggest that high-entropy tokens play an exceptionally important role in model training, since training with only the highest 20% entropy tokens yields significant performance gains. However, why such high-entropy tokens are beneficial remains insufficiently understood. In this work, we find that although high-entropy tokens within one answer tend to correlate with large gradient magnitude, entropy alone fails to consistently reflect token importance across different answers, considering the variations in the answer-level reward signals. Based on this observation, we introduce the Gradient Magnitude-based Token Selection (GMTS) method to quantify token importance, which leverages the entropy-gradient connection to approximate gradient-magnitude rankings for token selection. We find that training on the top 20% tokens ranked by GMTS consistently outperforms entropy-based token selection across three reasoning domains and various model sizes, suggesting that GMTS provides a more fine-grained estimate of token contribution for RLVR training.
@article{lv2026gmts, title = {{GMTS}: Gradient Magnitude-based Token Selection Improves {RLVR} Training for {LLM} Reasoning}, author = {Lv, Outongyi and Zhang, Yuanwei and Zhang, Xiaoqun}, journal = {arXiv preprint arXiv:2608.30632}, year = {2026}, month = aug, } - Conference
Physics-Augmented Graph Transformer for Multi-step Time-Domain Maxwell’s Equations in Electromagnetic Scattering
In Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2, Aug 2026@inproceedings{cao2026physicsaugmented, title = {Physics-Augmented Graph Transformer for Multi-step Time-Domain Maxwell's Equations in Electromagnetic Scattering}, author = {Cao, Huilin and Sun, Haoran and Liang, Jingwei and Li, Maokun and Ren, Yuxiang}, booktitle = {Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2}, pages = {10532--10542}, year = {2026}, month = aug, publisher = {ACM}, doi = {10.1145/3770855.3818937}, } - Preprint
Adaptive Dimension Reduction for Overlapping Group Sparsity
arXiv preprint arXiv:2601.20697, 2026Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting certain inherent low-dimensional structure of the sparse solution. In comparison, dimension reduction rules for overlapping group sparsity are generally less developed because the subgradient structure is more complex, making the link between sparsity pattern and the dual variable indirect due to the non-separability. In this work, we propose new dual certificates for overlapping group sparsity and a novel adaptive scheme for identifying the support of the overlapping group LASSO. We demonstrate how this scheme can be integrated into and significantly accelerate existing algorithms, including Primal-Dual splitting method, alternating direction method of multipliers and a recently developed variable projection scheme based on over-parameterization. We provide convergence analysis of the method and verify its practical effectiveness through experiments on standard datasets.
@article{bai2026adaptive, title = {Adaptive Dimension Reduction for Overlapping Group Sparsity}, author = {Bai, Yifan and Poon, Clarice and Liang, Jingwei}, journal = {arXiv preprint arXiv:2601.20697}, year = {2026}, } - Preprint
Formalization of Two Fixed-Point Algorithms in Hilbert Spaces
arXiv preprint arXiv:2602.17064, 2026Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel’skiĭ–Mann iteration and Halpern iteration are two widely used schemes. In this work, we formalize the convergence of these two fixed-point algorithms in the interactive theorem prover Lean4 based on type dependent theory. To this end, weak convergence and topological properties in the infinite-dimensional real Hilbert space are formalized. Definition and properties of nonexpansive operators are also provided. As a useful tool in convex analysis, we then formalize the Fejér monotone sequence. Building on these foundations, we verify the convergence of both the iteration schemes. Our formalization provides reusable components for machine-checked convergence analysis of fixed-point iterations and theories of convex analysis in real Hilbert spaces. Our code is available at https://github.com/TTony2019/fixed-point-iterations-in-lean.
@article{bai2026formalization, title = {Formalization of Two Fixed-Point Algorithms in Hilbert Spaces}, author = {Bai, Yifan and Li, Yantao and Yu, Jian and Liang, Jingwei}, journal = {arXiv preprint arXiv:2602.17064}, year = {2026}, } - Preprint
VeriScale: Adversarial Test-Suite Scaling for Verifiable Code Generation
arXiv preprint arXiv:2605.22368, 2026As large language models (LLMs) are increasingly deployed for software engineering, constructing high-quality benchmarks is crucial for evaluating not just the functional correctness, but also the formal verifiability of generated code. However, existing benchmarks are limited by the quantity and quality of positive and negative test cases, leading to an overestimation of model capabilities in generating specifications and implementations. To address this, we propose VeriScale, a novel framework driven by the adversarial implementations. It consists of two stages: test-suite expansion to construct diverse and challenging test cases, and test-suite reduction to distill them into compact yet discriminative suites. While VeriScale is general, we instantiate it on Verina to construct VerinaPlus, which expands the original test suites by over 83\times, and VerinaLite, a lightweight 14\times variant. Our experiments across eight state-of-the-art LLMs demonstrate that VerinaPlus exposes substantial model weaknesses hidden by the original benchmark, evidenced by sharp score drops on both SpecGen and CodeGen tasks, whereas VerinaLite maintains this discriminative power at a fraction of the evaluation cost. The enhanced benchmarks and source code are publicly available at https://github.com/XiaoyangLiu-sjtu/VeriScale.
@article{bai2026veriscale, title = {VeriScale: Adversarial Test-Suite Scaling for Verifiable Code Generation}, author = {Bai, Yifan and Liu, Xiaoyang and Mou, Zihao and Wang, Guihong and Yu, Jian and Xie, Shuhan and Li, Yantao and Zhang, Yangyu and Liang, Jingwei and Luo, Tao}, journal = {arXiv preprint arXiv:2605.22368}, year = {2026}, } - Conference
A Memory-Efficient Hierarchical Algorithm for Large-Scale Optimal Transport Problems
In The Fourteenth International Conference on Learning Representations (ICLR), 2026We propose HALO, a memory-efficient hierarchical algorithm for solving large-scale optimal transport (OT) problems with squared Euclidean cost, particularly effective in moderate-dimensional settings. The core of HALO lies in combining a hierarchical representation of the OT problem with parallel-friendly linear programming solvers, within which an active pruning technique is integrated to further reduce memory usage and computational cost. Theoretically, we establish a scale-independent iteration-complexity upper bound for the refinement phase, which is consistent with our numerical observations. Numerically, experiments on the image dataset and the 3D point cloud dataset demonstrate that HALO effectively alleviates the memory and scalability bottlenecks of existing solvers. Our method demonstrates significant advantages compared to state-of-the-art baselines: for images with n=1024^2 pixels, it achieves an 8.9\times speedup and 70.5% reduction in memory usage under comparable accuracy; for 3D point clouds at scale n=2^18, it achieves a 1.84\times speedup and an 83.2% reduction in memory usage with 24.9% lower transport cost.
@inproceedings{xia2026memory, title = {A Memory-Efficient Hierarchical Algorithm for Large-Scale Optimal Transport Problems}, author = {Xia, Wenzhou and Zhu, Ya-Nan and Liang, Jingwei and Zhang, Xiaoqun}, booktitle = {The Fourteenth International Conference on Learning Representations (ICLR)}, year = {2026}, } - Journal
Limiting Over-Smoothing and Over-Squashing of Graph Message Passing by Deep Scattering Transforms
Journal of Machine Learning Research, 2026Graph neural networks (GNNs) have become pivotal tools for processing graph-structured data, leveraging the message passing scheme as their core mechanism. However, traditional GNNs often grapple with issues such as instability, over-smoothing, and over-squashing, which can degrade performance and create a trade-off dilemma. In this paper, we introduce a discriminatively trained, multi-layer Deep Scattering Message Passing (DSMP) neural network designed to overcome these challenges. By harnessing spectral transformation, the DSMP model aggregates neighboring nodes with global information, thereby enhancing the precision and accuracy of graph signal processing. We provide theoretical proofs demonstrating the DSMP’s effectiveness in mitigating these issues under specific conditions. Additionally, we support our claims with empirical evidence and thorough frequency analysis, showcasing the DSMP’s superior ability to address instability, over-smoothing, and over-squashing.
@article{jiang2026limiting, title = {Limiting Over-Smoothing and Over-Squashing of Graph Message Passing by Deep Scattering Transforms}, author = {Jiang, Yuanhong and Zou, Dongmian and Zhang, Xiaoqun and Wang, Yu Guang}, journal = {Journal of Machine Learning Research}, year = {2026}, volume = {27}, number = {77}, pages = {1--39}, } - Journal
A Composed Alternating Relaxed Projection Algorithm for Convex Feasibility Problems
Journal of Scientific Computing, 2026Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating projection (MAP), and Douglas–Rachford splitting method (DR). The performance of the methods are governed by the geometric properties of the underlying sets. For example, the fixed-point sequence of the Douglas–Rachford splitting method exhibits a spiraling behavior when solving the feasibility problem of two subspaces, leading to a slow convergence speed and slower than MAP. However, when the problem at hand is non-polyhedral, DR can demonstrate significant faster performance. Motivated by the behaviors of the DR method, in this paper we propose a new algorithm for solving convex feasibility problems. The method is designed based on DR method by further incorporating a composition of projection and reflection. A non-stationary version of the method is also designed, aiming to achieve faster practical performance. Theoretical guarantees of the proposed schemes are provided and supported by numerical experiments.
@article{shen2025composed, title = {A Composed Alternating Relaxed Projection Algorithm for Convex Feasibility Problems}, author = {Shen, Yuting and Liang, Jingwei}, journal = {Journal of Scientific Computing}, volume = {109}, number = {2}, publisher = {Springer US}, year = {2026}, } - Journal
Model Consistency of the Iterative Regularization of Dual Ascent for Low-Complexity Regularization
Journal of Optimization Theory and Applications, 2026Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The former involves solving a variational optimization problem, which consists of a data-fidelity term and a regularization term, balanced by an appropriate weighting parameter. The latter mitigates overfitting to noise by selecting a suitable stopping time during the iterative process. A key topic in the study of regularization is the relationship between the regularized solution and the original ground truth. When the ground truth possesses a low-complexity structure referred to as the “model”, it can be shown that, under appropriate regularization promoting the same structure, the solution to the regularized problem is robust to small perturbations. This property is called “model consistency”. For variational regularization, model consistency in linear inverse problems has been studied in [42]. However, for iterative regularization, model consistency remains an open question. In this paper, building on recent developments in partial smoothness [42], we show that when the noise level is sufficiently small and an appropriate stopping criterion is used, iterative regularization is model consistent as well. Moreover, we show that the considered algorithm exhibits local linear behavior of the regularization. We provide numerical simulations to support our theoretical findings.
@article{gao2025model, title = {Model Consistency of the Iterative Regularization of Dual Ascent for Low-Complexity Regularization}, author = {Gao, Jie and Molinari, Cesare and Villa, Silvia and Liang, Jingwei}, journal = {Journal of Optimization Theory and Applications}, volume = {210}, number = {2}, publisher = {Springer US}, year = {2026}, } - Journal
A Stochastic Three-Block Alternating Minimization Algorithm and Its Application to Quantized Deep Neural Networks
CSIAM Transactions on Applied Mathematics, 2026Deep neural networks (DNNs) have made great progress in various fields. In particular, the quantized neural network is a promising technique making DNNs compatible on resource-limited devices for memory and computation saving. In this paper, we mainly consider a non-convex minimization model with three blocks to train quantized DNNs and propose a new stochastic three-block alternating minimization (STAM) algorithm to solve it. We develop a convergence theory for the STAM algorithm and obtain an ε-stationary point with optimal convergence rate \mathcalO(ε^-4). Furthermore, we apply our STAM algorithm to train DNNs with relaxed binary weights. The experiments are carried out on three different network structures, namely VGG-11, VGG-16 and ResNet-18. These DNNs are trained using two different data sets, CIFAR-10 and CIFAR-100, respectively. We compare our STAM algorithm with some classical efficient algorithms for training quantized neural networks. The test accuracy indicates the effectiveness of STAM algorithm for training relaxed binary quantization DNNs.
@article{bian2022stochastic, title = {A Stochastic Three-Block Alternating Minimization Algorithm and Its Application to Quantized Deep Neural Networks}, author = {Bian, Fengmiao and Liu, Ren and Zhang, Xiaoqun}, journal = {CSIAM Transactions on Applied Mathematics}, volume = {7}, number = {5}, pages = {1014--1046}, publisher = {Global Science Press}, year = {2026}, } - Conference
TRAC: Tensor-Train Based Across-Layer Compression for Parameter-Efficient Fine-Tuning
In The Fourteenth International Conference on Learning Representations (ICLR), 2026Fine-tuning large pre-trained models under resource constraints remains challenging due to the massive number of parameters involved. Existing parameter-efficient tuning methods, such as low-rank adaptation (LoRA) and its variants, rely heavily on matrix factorization and often struggle in extremely low-parameter regimes. In this work, we propose TRAC, a novel fine-tuning framework that leverages Tensor-Train decomposition with Across-layer Compression. Specifically, TRAC represents each adaptation module as a compact sequence of tensor-train cores and allows certain cores to be frozen or shared across layers, thereby exploiting the inherent similarity and redundancy among layer weight matrices. To retain layer-specific flexibility, lightweight controllers are introduced, enabling shared tensor cores to adaptively modulate representations. We evaluate TRAC on diverse architectures, including Qwen, LLaMA, GPT, BERT, and ViT, across benchmarks covering text classification, text generation, and image classification. Experimental results demonstrate that TRAC achieves performance comparable to or better than LoRA and its variants, while substantially reducing trainable parameters and storage requirements.
@inproceedings{ye2026trac, title = {TRAC: Tensor-Train Based Across-Layer Compression for Parameter-Efficient Fine-Tuning}, author = {Ye, Bangguo and Zhang, Yuanwei and Zhang, Xiaoqun}, booktitle = {The Fourteenth International Conference on Learning Representations (ICLR)}, year = {2026}, } - Journal
Exploring the Feasibility of Self-Supervised Learning for X-Ray Bone Image Analysis
Applied Mathematics for Modern Challenges, 2026The diverse tasks of X-ray bone image analysis necessitate training and maintaining numerous task-specific models. Recent advancements in foundation models have attracted extensive attention across various fields, promising significant improvements in medical applications. These models depend on large-scale datasets and utilize the self-supervised learning framework for their training. However, the study for the specific scenario when data acquisition is challenging still remains limited, such as the modality of bone X-ray images. This limitation is partly due to the limited availability of large-scale and curated bone X-ray datasets for research and model development. In this paper, we aim to fill this gap by applying DINO and DINOv2 frameworks for self-supervised learning across two bone X-ray image datasets. Our comprehensive analysis covers a range of downstream tasks, including supervised regression for accurate bone age assessment, unsupervised clustering through a Gaussian mixture model, and supervised regions of interest (ROI) localization. Our experiments demonstrate that pretrained models can significantly improve the downstream task performance and the extracted features conform to the property of bone age. The study shows the effectiveness of self-supervised learning on the bone X-ray images, providing insights into their capabilities to improve diagnostic precision and generalizability in medical imaging.
@article{zhao2026exploring, title = {Exploring the Feasibility of Self-Supervised Learning for X-Ray Bone Image Analysis}, author = {Zhao, Yuzhong and Ye, Bangguo and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {Applied Mathematics for Modern Challenges}, volume = {7}, pages = {1}, year = {2026}, } - Journal
Improving Out-Of-Distribution Detection in Normalizing Flows with Synthetic Outliers
Neurocomputing, 2026@article{zhao2026improving, title = {Improving Out-Of-Distribution Detection in Normalizing Flows with Synthetic Outliers}, author = {Zhao, Yuzhong and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {Neurocomputing}, pages = {133081}, year = {2026}, publisher = {Elsevier}, } - Journal
Enhancing Medical Imaging Out-Of-Distribution Detection with Synthetic Outliers
Journal of Mathematical Imaging and Vision, 2026The rapid advancement of deep learning in medical imaging necessitates reliable out-of-distribution (OOD) detection to ensure safe clinical deployment and prevent potential patient harm. Traditional supervised methods, which rely on closed-world assumptions, struggle in real-world scenarios where abnormal samples are both diverse and scarce. To address this, we propose a novel synthetic outlier-based OOD detection framework that distinguishes OOD samples without requiring real abnormal data. Our method generates a diverse and structurally plausible set of pseudo-outliers through a hybrid synthesis pipeline combining local and global transformations. By incorporating these synthetic outliers into a constrained optimization framework during training, our model learns a more discriminative decision boundary between in-distribution (ID) and OOD samples. We conducted extensive evaluations on four diverse medical imaging datasets, and the results show that our approach significantly outperforms state-of-the-art techniques in medical OOD detection while preserving high in-distribution classification accuracy. Our findings demonstrate that strategically generating synthetic outliers provides an effective and practical solution for enhancing model robustness in safety-critical medical applications.
@article{zhao2026enhancing, title = {Enhancing Medical Imaging Out-Of-Distribution Detection with Synthetic Outliers}, author = {Zhao, Yuzhong and Ding, Qiaoqiao and Ren, Haojie and Zhang, Xiaoqun}, journal = {Journal of Mathematical Imaging and Vision}, volume = {68}, number = {1}, pages = {1}, year = {2026}, publisher = {Springer US}, } - Journal
Robust Dynamic SPECT Reconstruction with Scarce Angular and Limited Temporal Sampling
Journal of Mathematical Imaging and Vision, 2026Reconstruction of dynamic single photon emission computed tomography (SPECT) images from a few angular projections is a challenging, ill-posed inverse problem. In addition, due to the high cost of image acquisition, previous works have mainly concentrated on restoring the dynamic images within a limited temporal sampling frequency, which raises the issue of low temporal resolution. In this paper, we propose a novel framework, Deep Spatial Prior with Continuous Temporal Representation (DSP-CTR), to reconstruct dynamic SPECT images with high resolution under scarce projection views and limited temporal sampling. Our method models SPECT image sequences by integrating a deep image prior for reconstructing the spatial structures and an implicit neural representation for learning time activity curves (TACs). Numerical experiments justify that the proposed method recovers high-quality image sequences from very few projection angles and time frames compared to the state-of-the-art methods.
@article{wu2026robust, title = {Robust Dynamic SPECT Reconstruction with Scarce Angular and Limited Temporal Sampling}, author = {Wu, Yicheng and He, Roy and Ding, Qiaoqiao and Zhang, Xiaoqun and Wang, Chao}, journal = {Journal of Mathematical Imaging and Vision}, volume = {68}, number = {3}, publisher = {Springer US}, year = {2026}, } - Journal
CT-Free Attenuation and Scatter Correction of [11C] CFT Brain PET Using a Bi-Directional Matching Network
NeuroImage, 2026• CT-free Bi-DPM (flow-ODE) enables emission-only PET ASC without pseudo-CT/MR. • Bi-DPM outperforms CycleGAN, Pix2Pix, and RF on MAE, PSNR, and SSIM. • Bi-DPM achieves high accuracy for striatal DAT quantification in DAT−/DAT+ cohorts. • This approach reduces radiation exposure by omitting CT scans. Quantitative PET imaging requires accurate attenuation and scatter correction (ASC), but the standard CT-based method introduces additional radiation exposure—a significant concern for neurological studies involving repeated scans. Here we applied and extended a CT-free deep learning framework for [ 11 C]CFT brain PET that achieves diagnostic-comparable dopamine transporter (DAT) quantification while avoiding CT-associated radiation. A Bi-directional Discrete Process Matching (Bi-DPM) network was adapted to establish reversible transformations between non-corrected (NASC-PET) and fully corrected (ASC-PET) images through discrete consistency constraints, eliminating the need for pseudo-CT generation or anatomical priors. Evaluated on 90 Parkinsonian syndrome patients, Bi-DPM demonstrated superior performance to Cycle-Consistent Generative Adversarial Networks (CycleGAN), Pix2Pix, and Rectified Flow (RF) across quantitative metrics (lower MAE, higher PSNR/SSIM). For standardized uptake value mean (SUVmean) measurements, Bi-DPM showed excellent agreement with CT-ASC reference (CCC > 0.98, PCC > 0.98). Voxel-wise analysis of DAT-positive/-negative (DAT+/DAT−) groups confirmed Bi-DPM’s clinical validity, with statistical significance maps closely aligned to CT-ASC (Dice = 0.953 vs. 0.938 for RF, 0.948 for Pix2Pix and 0.618 for CycleGAN). This approach reduces unnecessary radiation exposure by omitting CT scans while maintaining PET quantification accuracy.
@article{ding2026ctfree, title = {CT-Free Attenuation and Scatter Correction of [11C] CFT Brain PET Using a Bi-Directional Matching Network}, author = {Ding, Wenxiang and Sun, Xiaolin and Ding, Qiaoqiao and Tan, Xiaoyue and Zhang, Qing and He, Shanzhen and Li, Peiyong and Huang, Qiu and Zhang, Xiaoqun and Jiang, Lei}, journal = {NeuroImage}, pages = {121721}, year = {2026}, publisher = {Academic Press}, } - Journal
A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Recovery
Journal of Scientific Computing, 2026This paper focuses on recovering a low-multilinear-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single-Mode Quasi Riemannian Gradient Descent (SM-QRGD) method. The SM-QRGD algorithm integrates the strengths of the fixed-rank matrix tangent space projection and the sequentially truncated high-order singular value decomposition (ST-HOSVD). This hybrid approach enables SM-QRGD to attain computational complexity per iteration of 3 n^d r , where n and r represent the tensor’s size and multilinear rank. This leads to a reduced computation cost per iteration, compared to other methods with the complexity coefficient related to the tensor order d . Theoretically, we establish the convergence of SM-QRGD through the Tensor Restricted Isometry Property (TRIP) and the structural properties of the fixed-rank matrix manifold. On the practical side, a comprehensive range of experiments validates the accuracy and efficacy of the proposed algorithm SM-QRGD for low-multilinear-rank tensor recovery.
@article{zhang2026singlemode, title = {A Single-Mode Quasi Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Recovery}, author = {Zhang, Yuanwei and Zhu, Ya-Nan and Zhang, Xiaoqun}, journal = {Journal of Scientific Computing}, volume = {106}, number = {1}, pages = {23}, year = {2026}, publisher = {Springer US}, } - Journal
Few-Shot Multi-Task Learning of Linear Invariant Features with Meta Subspace Pursuit
CSIAM Transactions on Applied Mathematics, 2026Data scarcity poses a serious threat to modern machine learning and artificial intelligence, as their practical success typically relies on the availability of big datasets. One effective strategy to mitigate the issue of insufficient data is to first harness information from other data sources possessing certain similarities in the study design stage, and then employ the multi-task or meta learning framework in the analysis stage. In this paper, we focus on multi-task (or multi-source) linear models whose coefficients across tasks share an invariant low-rank component, a popular structural assumption considered in the recent multi-task or meta learning literature. Under this assumption, we propose a new algorithm, called meta subspace pursuit (Meta-SP), that provably learns this invariant subspace shared by different tasks. Under this stylized setup for multi-task or meta learning, we establish both the algorithmic and statistical guarantees of the proposed method. Extensive numerical experiments are conducted, comparing Meta-SP against several competing methods, including popular, off-the-shelf model-agnostic meta learning algorithms such as almost-no-inner-loop algorithm. These experiments demonstrate that Meta-SP achieves superior performance over the competing methods in various aspects.
@article{zhang2024fewshot, title = {Few-Shot Multi-Task Learning of Linear Invariant Features with Meta Subspace Pursuit}, author = {Zhang, Chaozhi and Liu, Lin and Zhang, Xiaoqun}, journal = {CSIAM Transactions on Applied Mathematics}, volume = {7}, number = {6}, pages = {1156--1191}, publisher = {Global Science Press}, year = {2026}, }
2025
- Journal
A Guide to Stochastic Optimisation for Large-Scale Inverse Problems
Inverse Problems, 2025Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs, while still ensuring significant progress towards the solution. Driven by the need to solve large-scale optimisation problems as efficiently as possible, the last decade has witnessed an explosion of research in this area. Leveraging the parallels between machine learning and inverse problems has allowed harnessing the power of this research wave for solving inverse problems. In this survey, we provide a comprehensive account of the state-of-the-art in stochastic optimisation from the viewpoint of variational regularisation for inverse problems where the solution is modelled as minimising an objective function. We present algorithms with diverse modalities of problem randomisation and discuss the roles of variance reduction, acceleration, higher-order methods, and other algorithmic modifications, and compare theoretical results with practical behaviour. We focus on the potential and the challenges for stochastic optimisation that are unique to variational regularisation for inverse imaging problems and are not commonly encountered in machine learning. We conclude the survey with illustrative examples from imaging on linear inverse problems to examine the advantages and disadvantages that this new generation of algorithms bring to the field of inverse problems.
@article{ehrhardt2024guide, title = {A Guide to Stochastic Optimisation for Large-Scale Inverse Problems}, author = {Ehrhardt, Matthias J. and Kereta, Zeljko and Liang, Jingwei and Tang, Junqi}, journal = {Inverse Problems}, volume = {41}, number = {5}, pages = {053001}, year = {2025}, publisher = {IOP Publishing}, } - Journal
Physics-Data Hybrid Driven Edge-Featured Graph Attention Networks for Surface Currents Learning of 3D PEC Targets
IEEE Transactions on Antennas and Propagation, 2025To achieve fast and accurate modeling of electrically large targets, this paper proposes a physics-data hybrid driven surface current learning method (PdEgatSCL), which can learn combined field integral operator and achieve end-to-end solving from incident fields to surface currents. The edge-feature graph attention network (EGAT) is employed as the foundational architecture of PdEgatSCL, where the Green’s function and its divergence are explicitly encoded as edge features into the network. The attention mechanism of EGAT is leveraged to model the scattering characteristics of the targets. Additionally, the center coordinates and area of the discretized surface elements are input as node features to ensure that the mesh information is fully utilized. Finally, PdEgatSCL is applied to solve the surface currents of three-dimensional perfect electric conductor (PEC) targets. Numerical results demonstrate that the surface current solutions obtained by PdEgatSCL align well with the ground truth computed by the Method of Moments (MoM). Moreover, compared to SOTA AI-based method, PdEgatSCL exhibits higher accuracy while accelerating the average inference time by 87.67% and reducing memory consumption by 99.24%.
@article{cao2025physics, title = {Physics-Data Hybrid Driven Edge-Featured Graph Attention Networks for Surface Currents Learning of 3D PEC Targets}, author = {Cao, Huilin and Sun, Haoran and Liang, Jingwei and Shan, Tao and Ren, Yuxiang and Li, Maokun}, journal = {IEEE Transactions on Antennas and Propagation}, year = {2025}, publisher = {IEEE}, } - Journal
Deep Equilibrium Model with Weighted Densely-Connected Iteration Differences for Convergent Image Restoration
IEEE Journal of Selected Topics in Signal Processing, 2025Deep equilibrium models (DEMs) are emerging as an efficient alternative to train deep unrolling networks (DUNs) realized by recasting iterative optimization algorithms for image restoration (IR) in a single iteration using constant memory usage and are potential to allow infinite iterations until convergence to fixed points. However, existing DEMs for IR suffer from architectural constraints in exploiting skip connections and adaptive parameters varying with iterations to simultaneously benefit feature learning and achieve stable reconstruction with theoretical convergence guarantees. To address these challenges, we formulate a novel IR optimization problem with a deep neural network (DNN)-based energy and propose DenseDiff, a DEM based on proximal gradient descent with weighted densely-connected iteration differences, to solve it. Specifically, for each iteration, we combine densely connected iteration differences from preceding iterations with adaptive weights and step sizes to facilitate feature learning, and reformulate multi-variable fixed-point computation as a two-variable problem to preserve the effective parameter space for optimization. Furthermore, we thoroughly explore the properties of common DNN components for theoretical guidance for constituting the energy in practice, and demonstrate that DenseDiff converges to a critical point of the objective function with at least a sublinear rate. Comprehensive evaluations on image deblurring, inpainting, and CS-MRI reveal that DenseDiff achieves state-of-the-art reconstruction performance with guaranteed convergence, suggesting a promising paradigm for designing interpretable DNNs for IR tasks.
@article{zheng2025deep, title = {Deep Equilibrium Model with Weighted Densely-Connected Iteration Differences for Convergent Image Restoration}, author = {Zheng, Ziyang and Dai, Wenrui and Liang, Jingwei and Peng, Xinyu and Xue, Duoduo and Xiong, Hongkai}, journal = {IEEE Journal of Selected Topics in Signal Processing}, year = {2025}, publisher = {IEEE}, } - Preprint
Partial Smoothness, Subdifferentials and Set-Valued Operators
arXiv preprint arXiv:2501.15540, 2025Over the past decades, the concept "partial smoothness" has been playing as a powerful tool in several fields involving nonsmooth analysis, such as nonsmooth optimization, inverse problems and operation research, etc. The essence of partial smoothness is that it builds an elegant connection between the optimization variable and the objective function value through the subdifferential. Identifiability is the most appealing property of partial smoothness, as locally it allows us to conduct much finer or even sharp analysis, such as linear convergence or sensitivity analysis. However, currently the identifiability relies on non-degeneracy condition and exact dual convergence, which limits the potential application of partial smoothness. In this paper, we provide an alternative characterization of partial smoothness through only subdifferentials. This new perspective enables us to establish stronger identification results, explain identification under degeneracy and non-vanishing error. Moreover, we can generalize this new characterization to set-valued operators, and provide a complement definition of partly smooth operator proposed in [14].
@article{qin2025partial, title = {Partial Smoothness, Subdifferentials and Set-Valued Operators}, author = {Qin, Ziqi and Liang, Jingwei}, journal = {arXiv preprint arXiv:2501.15540}, year = {2025}, } - Journal
A Variable Metric Extrapolation Proximal Iterative Hard Thresholding Method
Journal of the Operations Research Society of China, 2025In this paper, we consider the \ell_0 minimization problem whose objective function is the sum of \ell_0-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton method, named variable metric extrapolation proximal iterative hard thresholding (VMEPIHT) method, is proposed. Then we analyze its convergence, linear convergence rate and superlinear convergence rate under appropriate assumptions. Finally, we conduct numerical experiments on compressive sensing problem and CT image reconstruction problem to confirm VMPIHT method’s efficiency, compared with other state-of-art methods.
@article{zhang2021variable, title = {A Variable Metric Extrapolation Proximal Iterative Hard Thresholding Method}, author = {Zhang, Xue and Zhang, Xiaoqun}, journal = {Journal of the Operations Research Society of China}, volume = {13}, number = {1}, pages = {161--183}, publisher = {Springer}, year = {2025}, } - Journal
Dynamic PET Image Reconstruction via Non-Negative INR Factorization
SIAM Journal on Imaging Sciences, 2025The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, non-negative implicit neural representation factorization, based on low rank matrix factorization of unknown images and employing neural networks to represent both coefficients and bases. Mathematically, we demonstrate that if a sequence of dynamic PET images satisfies a generalized non-negative low-rank property, it can be decomposed into a set of non-negative continuous functions varying in the temporal-spatial domain. This bridges the well-established non-negative matrix factorization with continuous functions, and we propose using implicit neural representations to connect matrix with continuous functions. The neural network parameters are obtained by minimizing the KL divergence, with additional sparsity regularization on coefficients and bases. Extensive experiments on dynamic PET reconstruction with Poisson noise demonstrate the effectiveness of the proposed method compared to other methods while giving continuous representations for object’s detailed geometric features and regional concentration variation.
@article{zhang2025dynamicpet, title = {Dynamic PET Image Reconstruction via Non-Negative INR Factorization}, author = {Zhang, Chaozhi and Ding, Wenxiang and He, Roy Y and Zhang, Xiaoqun and Ding, Qiaoqiao}, journal = {SIAM Journal on Imaging Sciences}, volume = {18}, number = {4}, pages = {2206--2235}, year = {2025}, publisher = {Society for Industrial and Applied Mathematics}, } - Conference
Preconditioned Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Completion
In Forty-second International Conference on Machine Learning (ICML), 2025Tensors play a crucial role in numerous scientific and engineering fields. This paper addresses the low-multilinear-rank tensor completion problem, a fundamental task in tensor-related applications. By exploiting the manifold structure inherent to the fixed-multilinear-rank tensor set, we introduce a simple yet highly effective preconditioned Riemannian metric and propose the Preconditioned Riemannian Gradient Descent (PRGD) algorithm. Compared to the standard Riemannian Gradient Descent (RGD), PRGD achieves faster convergence while maintaining the same order of per-iteration computational complexity. Theoretically, we provide the recovery guarantee for PRGD under near-optimal sampling complexity. Numerical results highlight the efficiency of PRGD, outperforming state-of-the-art methods on both synthetic data and real-world video inpainting tasks.
@inproceedings{zhang2025preconditioned, title = {Preconditioned Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Completion}, author = {Zhang, Yuanwei and Bian, Fengmiao and Zhang, Xiaoqun and Cai, Jian-Feng}, booktitle = {Forty-second International Conference on Machine Learning (ICML)}, year = {2025}, } - Journal
Personalized Artifacts Modeling and Federated Learning for Multi-Institutional Low-Dose CT Reconstruction
Inverse Problems and Imaging, 2025The clinical utility of Computed Tomography (CT) is widely acknowledged, but its potential radiation risk has raised public concerns. In recent years, deep learning based methods emerged as a powerful tool for low-dose CT (LDCT) reconstruction. In a multi-institution centralized learning scenario, it often requires the centralized collection of a significant amount of data. Federated learning (FL) can be used to improve data privacy and efficiency in CT image reconstruction by enabling multiple institutions to collaborate without needing to aggregate local data. However, the statistical heterogeneity caused by different CT scanning protocols can substantially degrade the performance of FL models. Recent FL techniques tend to solve this by enhancing the generalization of the global model, but they ignore the domain-specific features, which may contain important information for local reconstruction. In our paper, we propose a personalized FL algorithm for CT image reconstruction (PerFed-LDCT). The core idea is to construct an image-artifact fusion network which is divided into two parts: a client-specific model for extracting the domain-specific artifacts, and a globally-shared model for generalized image reconstruction. Moreover, to further boost the convergence of our FL model when a domain shift is present, a weighted artifact regularization term is introduced to directly correct any deviation of local artifact estimation during optimization. The whole framework can be implemented in a distributed manner and various experiments show that our method achieved an improved performance compared to other state-of-the-art methods.
@article{xu2025personalized, title = {Personalized Artifacts Modeling and Federated Learning for Multi-Institutional Low-Dose CT Reconstruction}, author = {Xu, Jingbo and Zhu, Ya-Nan and Zhang, Xiaoqun and Ding, Qiaoqiao}, journal = {Inverse Problems and Imaging}, volume = {19}, number = {5}, pages = {858--876}, year = {2025}, publisher = {Inverse Problems and Imaging}, } - Journal
Bayesian Compressive Sensing Using Generative Models
Inverse Problems, 2025Generative models, used to create new data resembling a given dataset, have achieved notable success in image reconstruction, especially in scenarios involving incomplete or noisy measurements. In Bayesian compressive sensing (CS) and more broadly in Bayesian inverse problems, the posterior inference of unknown quantities plays a crucial role, as it enables the incorporation of prior knowledge, handles ill-posedness, and provides a principled way to quantify uncertainty. However, it encounters challenges with high-dimensional inverse problems and complex prior distributions that are challenging to represent mathematically in traditional Bayesian frameworks. In this paper, we leverage generative models to establish variational inference for posterior mean (PM) estimation in Bayesian CS. The PM estimation is demonstrated to be straightforward and offers theoretical guarantees for Bayesian CS. Our proposed method, incorporating reparameterization techniques and variational approximations, not only significantly enhances reconstruction quality but also demonstrates robust performance in experiments on CS and magnetic resonance imaging reconstruction.
@article{zhang2025bayesian, title = {Bayesian Compressive Sensing Using Generative Models}, author = {Zhang, Ying and Zhang, Xiaoqun and Liu, Jiulong}, journal = {Inverse Problems}, volume = {41}, number = {8}, pages = {085009}, year = {2025}, publisher = {IOP Publishing}, } - Journal
Multi-Scale Frequency-Enhanced Deep D-Bar Method for Electrical Impedance Tomography
Inverse Problems, 2025The regularized D-bar method is a popular method for solving electrical impedance tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve the associated D-bar integral equations, yielding a smooth conductivity approximation. However, the D-bar reconstruction often presents low contrast and resolution due to the absence of accurate high-frequency information and the ill-posedness of the problem. In this paper, we propose a deep learning-based supervised approach for real-time EIT reconstruction. Based on the D-bar method, we propose to utilize both multi-scale frequency enhancement and spatial consistency for a high-image-quality reconstruction. Additionally, we propose a fixed-point iteration for solving discrete D-bar systems on GPUs for fast computation. Numerical results are performed for both the continuum model and complete electrode model simulation on KIT4 and ACT4 datasets to demonstrate notable improvements in absolute EIT imaging quality.
@article{cao2025multiscale, title = {Multi-Scale Frequency-Enhanced Deep D-Bar Method for Electrical Impedance Tomography}, author = {Cao, Xiang and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {41}, number = {8}, pages = {085005}, year = {2025}, publisher = {IOP Publishing}, } - Preprint
Diff-Ano: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators
arXiv preprint arXiv:2507.16344, 2025Ultrasound Computed Tomography (USCT) constitutes a nonlinear inverse problem with inherent ill-posedness that can benefit from regularization through diffusion generative priors. However, traditional approaches for solving Helmholtz equation-constrained USCT face three fundamental challenges when integrating these priors: PDE-constrained gradient computation, discretization-induced approximation errors, and computational imbalance between neural networks and numerical PDE solvers. In this work, we introduce Diff-ANO (Diffusion-based Models with Adjoint Neural Operators), a novel framework that combines conditional consistency models with adjoint operator learning to address these limitations. Our two key innovations include: (1) a conditional consistency model that enables measurement-conditional few-step sampling by directly learning a self-consistent mapping from diffusion trajectories, and (2) an adjoint operator learning module that replaces traditional PDE solvers with neural operator surrogates for efficient adjoint-based gradient computation. To enable practical deployment, we introduce the batch-based Convergent Born Series (BCBS)–a memory-efficient strategy for online generation of neural operator training pairs. Comprehensive experiments demonstrate that Diff-ANO significantly improves both computational efficiency and reconstruction quality, especially under sparse-view and partial-view measurement scenarios.
@article{cao2025diffano, title = {Diff-Ano: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators}, author = {Cao, Xiang and Ding, Qiaoqiao and Liu, Xinliang and Zhang, Lei and Zhang, Xiaoqun}, journal = {arXiv preprint arXiv:2507.16344}, year = {2025}, } - Journal
Subspace Diffusion Posterior Sampling for Travel-Time Tomography
Inverse Problems, 2025Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical solvers for gradient updates. Although diffusion-based sampling methods can produce high-quality reconstructions, challenges persist in nonlinear PDE-based inverse problems and sampling speed. In this work, we explore solving PDE-based travel-time tomography based on subspace diffusion generative models. Our main contributions are twofold: first, we propose a posterior sampling process for PDE-based inverse problems by solving the associated adjoint-state equation in a plug-and-play fashion. Second, we present a subspace-based dimension reduction technique, enabling solving PDE-based inverse problems from coarse to refined grids, for conditional sampling acceleration. Our numerical experiments showed satisfactory advancements in improving the travel-time imaging quality and reducing the sampling time for reconstruction.
@article{cao2025subspace, title = {Subspace Diffusion Posterior Sampling for Travel-Time Tomography}, author = {Cao, Xiang and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {41}, number = {5}, pages = {055010}, year = {2025}, publisher = {IOP Publishing}, } - Journal
EESyn-CTP: Edge-End Collaboration for Patient-Friendly CTP Image Synthesis
IEEE Internet of Things Journal, 2025In the field of medical imaging driven by the Internet of Things (IoT), with the rapid growth of the number of medical devices and the widespread application of edge computing (EC) technology, efficient collaborative computing on resource-constrained end medical devices has become the key to improving diagnostic efficiency, thereby bringing a more patient-friendly diagnosis and treatment experience. Computed tomography perfusion (CTP) images play an irreplaceable role in the assessment of brain tissue ischemia in patients with acute ischemic stroke (AIS), with high diagnostic accuracy in identifying ischemic lesions and distinguishing infarction from penumbra, but it has the disadvantages of high radiation dose and high cost. To this end, we propose a CTP image synthesis framework based on edge-end collaboration (EESyn-CTP), which aims to use non-contrast CT (NCCT), CT angiography (CTA), and delayed CTA (CTA+8s) images to synthesize CTP images with arbitrary time to optimize AIS diagnosis. The framework consists of two stages: the pre-training stage on the edge server and the fine-tuning stage on the end device. Specifically, we first deploy a temporal residual generative network, t-UNet, on the edge server for pre-training. This process utilizes multiple CTP images, which share similar perfusion features with CTA, CTA+8s, and NCCT images, to effectively learn the gap in perfusion information between the inputs and outputs. Subsequently, the pre-trained t-UNet model parameters are frozen and broadcast to the edge medical device. A UNet adapter is introduced before the model, and fine-tuning is performed on the adapter weights using real NCCT, CTA, and CTA+8s images as input. This approach facilitates the synthesis of CTP images at arbitrary time points. Finally, experiments on an internal data set showed that the quality of Syn-CTP images synthesized by the EESyn-CTP framework is comparable to that of real CTP images and significantly reduces computation latency and energy overhead.
@article{wang2025eesyn, title = {EESyn-CTP: Edge-End Collaboration for Patient-Friendly CTP Image Synthesis}, author = {Wang, Yihao and Zhang, Yu and Qiao, Dewen and Guo, Songtao and Liu, Yu and Zhao, Chenhao and Gu, Tao and Ding, Qiaoqiao and Zhang, Xiaoqun and Chen, Xuetao}, journal = {IEEE Internet of Things Journal}, year = {2025}, publisher = {IEEE}, } - Journal
Un-Evaluated Solutions May Be Valuable in Expensive Optimization
Swarm and Evolutionary Computation, 2025Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary algorithms (SAEAs) in EOPs, we discovered an intriguing phenomenon. Because only a limited number of solutions are evaluated in each iteration, relying solely on these evaluated solutions for evolution can lead to reduced disparity in successive populations. This, in turn, hampers the reproduction operators’ ability to generate superior solutions, thereby reducing the algorithm’s convergence speed. To address this issue, we propose a strategic approach that incorporates high-quality, un-evaluated solutions predicted by surrogate models during the selection phase. This approach aims to improve the distribution of evaluated solutions, thereby generating a superior next generation of solutions. This work details specific implementations of this concept across various reproduction operators and validates its effectiveness using multiple surrogate models. Experimental results demonstrate that the proposed strategy significantly enhances the performance of surrogate-assisted evolutionary algorithms. Compared to mainstream SAEAs and Bayesian optimization algorithms, our approach incorporating the un-evaluated solution strategy shows a marked improvement.
@article{hao2025unevaluated, title = {Un-Evaluated Solutions May Be Valuable in Expensive Optimization}, author = {Hao, Hao and Zhang, Xiaoqun and Zhou, Aimin}, journal = {Swarm and Evolutionary Computation}, volume = {94}, pages = {101905}, year = {2025}, publisher = {Elsevier}, } - Journal
Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-Based Approach Integrating Maximum Mean Discrepancy and Optimal Transport
SIAM Journal on Imaging Sciences, 2025Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation, and statistical inference. One powerful framework for such transformations is normalizing flow, which transforms an unknown distribution into a standard normal distribution using an invertible network. In this paper, we introduce a novel model called SyMOT-Flow, which trains an invertible transformation by minimizing the symmetric maximum mean discrepancy between samples from two unknown distributions, and an optimal transport cost is incorporated as regularization to obtain a short-distance and interpretable transformation. The resulting transformation leads to more stable and accurate sample generation. Several theoretical results are established for the proposed model, and its effectiveness is validated with illustrative low-dimensional examples as well as high-dimensional bimodality medical image generation through the forward and reverse flows.
@article{xiong2025symot, title = {Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-Based Approach Integrating Maximum Mean Discrepancy and Optimal Transport}, author = {Xiong, Zhe and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {SIAM Journal on Imaging Sciences}, volume = {18}, number = {1}, pages = {570--596}, year = {2025}, publisher = {Society for Industrial and Applied Mathematics}, } - Journal
Flash Proton Radiation Therapy via a Stochastic Three-Operator Splitting Method
Inverse Problems, 2025The inverse radiation therapy planning problem is crucial in achieving tumoricidal doses while minimizing radiation-induced normal-tissue toxicity. Compared to conventional radiation therapy (with conventional dose rates), flash proton radiation therapy (with ultra-high dose rates) can provide additional normal tissue sparing. However, this groundbreaking advancement in radiation oncology introduces a challenging nonconvex and nonsmooth optimization problem. In this paper, we propose a stochastic three-operator splitting (STOS) algorithm to address the flash proton radiation therapy problem. We establish the convergence and convergence rates of the STOS algorithm under the nonconvex framework for both unbiased gradient estimators and variance-reduced gradient estimators. These stochastic gradient estimators include the most popular ones, such as SGD, SAGA, SARAH, and SAG, among others. Experimental results demonstrate that the flash proton radiation therapy plans obtained by the STOS algorithm can effectively kill tumors while better protecting normal tissues.
@article{bian2025flash, title = {Flash Proton Radiation Therapy via a Stochastic Three-Operator Splitting Method}, author = {Bian, Fengmiao and Liu, Jiulong and Zhang, Xiaoqun and Gao, Hao and Cai, Jian-Feng}, journal = {Inverse Problems}, volume = {41}, number = {2}, pages = {025007}, year = {2025}, publisher = {IOP Publishing}, } - Journal
Expensive Optimization via Relation
IEEE Transactions on Evolutionary Computation, 2025Expensive optimization problems pose significant challenges to traditional gradient-free optimization due to their costly evaluation overhead. Surrogate model-assisted evolutionary optimization, which substitutes expensive evaluation functions with surrogate models, can effectively overcome these challenges. However, designing an efficient surrogate model is the key issue in model-assisted evolutionary optimization. In recent years, establishing surrogate models through the relationships between solutions has become a promising modeling strategy, following regression and classification models. Yet, there has been no systematic organization or summary of relation models. Therefore, this paper views the relation as a perspective to outline the development context of this field, defines the framework for researching relation models, and reviews typical strategies under each framework. Finally, it validates the effectiveness of numerous strategies through experiments. The entire strategy collection will be open-sourced on GitHub , making it easier for more researchers to participate in this field of study.
@article{hao2025relation, title = {Expensive Optimization via Relation}, author = {Hao, Hao and Zhang, Xiaoqun and Zhou, Aimin}, journal = {IEEE Transactions on Evolutionary Computation}, year = {2025}, publisher = {IEEE}, } - Journal
Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models
Medical Image Analysis, 2025Reconstructing high-fidelity magnetic resonance (MR) images from under-sampled k-space is a commonly used strategy to reduce scan time. The posterior sampling of diffusion models based on the real measurement data holds significant promise of improved reconstruction accuracy. However, traditional posterior sampling methods often lack effective data consistency guidance, leading to inaccurate and unstable reconstructions. Implicit neural representation (INR) has emerged as a powerful paradigm for solving inverse problems by modeling a signal’s attributes as a continuous function of spatial coordinates. In this study, we present a novel posterior sampler for diffusion models using INR, named DiffINR. The INR-based component incorporates both the diffusion prior distribution and the MRI physical model to ensure high data fidelity. DiffINR demonstrates superior performance on in-distribution datasets with remarkable accuracy, even under high acceleration factors (up to R = 12 in single-channel reconstruction). Furthermore, DiffINR exhibits excellent generalizability across various tissue contrasts and anatomical structures with low uncertainty. Overall, DiffINR significantly improves MRI reconstruction in terms of accuracy, generalizability and stability, paving the way for further accelerating MRI acquisition. Notably, our proposed framework can be a generalizable framework to solve inverse problems in other medical imaging tasks.
@article{chu2025highly, title = {Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models}, author = {Chu, Jiayue and Du, Chenhe and Lin, Xiyue and Zhang, Xiaoqun and Wang, Lihui and Zhang, Yuyao and Wei, Hongjiang}, journal = {Medical Image Analysis}, volume = {100}, pages = {103398}, year = {2025}, publisher = {Elsevier}, } - Preprint
Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent
arXiv preprint arXiv:2501.13385, 2025Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in handling structured high-order tensors, this paper investigates the low-rank tensor completion problem based on the TT-format. We proposed a preconditioned Riemannian gradient descent algorithm (PRGD) to solve low TT-rank tensor completion and establish its linear convergence. Experimental results on both simulated and real datasets demonstrate the effectiveness of the PRGD algorithm. On the simulated dataset, the PRGD algorithm reduced the computation time by two orders of magnitude compared to existing classical algorithms. In practical applications such as hyperspectral image completion and quantum state tomography, the PRGD algorithm significantly reduced the number of iterations, thereby substantially reducing the computational time.
@article{bian2025tensortrain, title = {Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent}, author = {Bian, Fengmiao and Cai, Jian-Feng and Zhang, Xiaoqun and Zhang, Yuanwei}, journal = {arXiv preprint arXiv:2501.13385}, year = {2025}, } - Journal
A Fully Automated U-Net Based ROIs Localization and Bone Age Assessment Method
Mathematical Biosciences and Engineering, 2025Bone age assessment (BAA) is a widely used clinical practice for the biological development of adolescents. The Tanner Whitehouse (TW) method is a traditionally mainstream method that manually extracts multiple regions of interest (ROIs) related to skeletal maturity to infer bone age. In this paper, we propose a deep learning-based method for fully automatic ROIs localization and BAA. The method consists of two parts: a U-net-based backbone, selected for its strong performance in semantic segmentation, which enables precise and efficient localization without the need for complex pre- or post-processing. This method achieves a localization precision of 99.1% on the public RSNA dataset. Second, an InceptionResNetV2 network is utilized for feature extraction from both the ROIs and the whole image, as it effectively captures both local and global features, making it well-suited for bone age prediction. The BAA neural network combines the advantages of both ROIs-based methods (TW3 method) and global feature-based methods (GP method), providing high interpretability and accuracy. Numerical experiments demonstrate that the method achieves a mean absolute error (MAE) of 0.38 years for males and 0.45 years for females on the public RSNA dataset, and 0.41 years for males and 0.44 years for females on an in-house dataset, validating the accuracy of both localization and prediction.
@article{zhao2025boneage, title = {A Fully Automated U-Net Based ROIs Localization and Bone Age Assessment Method}, author = {Zhao, Yuzhong and Wang, Yihao and Yuan, Haolei and Xie, Weiwei and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {Mathematical Biosciences and Engineering}, volume = {22}, number = {1}, pages = {138--151}, year = {2025}, publisher = {American Institute of Mathematical Sciences}, }
2024
- Journal
Federated Primal-Dual Fixed Point Algorithm
SIAM Journal on Mathematics of Data Science, 2024Federated learning (FL) is a distributed learning paradigm that allows several clients to learn a global model without sharing their private data. In this paper, we generalize a primal dual fixed point (PDFP) \citePDFP method to federated learning setting and propose an algorithm called Federated PDFP (FPDFP) for solving composite optimization problems. In addition, a quantization scheme is applied to reduce the communication overhead during the learning process. An O(1/k) convergence rate (where is the communication round) of the proposed FPDFP is provided. Numerical experiments, including graph-guided logistic regression, 3D Computed Tomography (CT) reconstruction are considered to evaluate the proposed algorithm.
@article{zhu2023federated, title = {Federated Primal-Dual Fixed Point Algorithm}, author = {Zhu, Ya-Nan and Liang, Jingwei and Zhang, Xiaoqun}, journal = {SIAM Journal on Mathematics of Data Science}, volume = {6}, number = {4}, pages = {1138--1172}, year = {2024}, publisher = {Society for Industrial and Applied Mathematics}, } - Journal
A Scalable Sphere-Constrained Magnitude-Sparse SAR Imaging
Journal of Nonlinear & Variational Analysis, 2024The classical synthetic aperture radar (SAR) imaging techniques based on matched filters are limited by data bandwidth, resulting in limited imaging performance with side lobes and speckles present. To address the high-resolution SAR imaging problem, sparse reconstruction has been extensively investigated. However, the state-of-the-art sparse recovery methods seldom consider the complex-valued reflectivity of the scene and only recover an approximated real-valued scene instead. Furthermore, iterative schemes associated with the sparse recovery methods demand a high computational cost, which limits the practical applications of these methods. In this paper, we establish a sphere-constrained magnitude-sparsity SAR imaging model, aiming at enhancing the SAR imaging quality with high efficiency. We propose a non-convex non-smooth optimization method, which can be accelerated by stochastic average gradient acceleration to be scalable with large-scale problems. Numerical experiments are conducted with point-target and extended-target simulations. On the one hand, the point-target simulation showcases the superiority of our proposed method over the classical methods in terms of resolution. On the other hand, the extended-target simulation with random phases is considered to be in line with the practical scenario, and the results demonstrate that our method outperforms the classical SAR imaging methods and sparse recovery without phase prior in terms of PSNR. Meanwhile, owing to the stochastic acceleration, our method is faster than the existing sparse recovery methods by orders of magnitude.
@article{jiang2024scalable, title = {A Scalable Sphere-Constrained Magnitude-Sparse SAR Imaging}, author = {Jiang, Ming and Qu, Jiaxuan and Ding, Jinshan and Liang, Jingwei}, journal = {Journal of Nonlinear \& Variational Analysis}, volume = {8}, number = {3}, year = {2024}, } - Journal
Automatic Recognition of White Blood Cell Images with Memory Efficient Superpixel Metric GNN: SMGNN
Mathematical Biosciences and Engineering, 2024An automatic recognizing system of white blood cells can assist hematologists in the diagnosis of many diseases, where accuracy and efficiency are paramount for computer-based systems. In this paper, we presented a new image processing system to recognize the five types of white blood cells in peripheral blood with marked improvement in efficiency when juxtaposed against mainstream methods. The prevailing deep learning segmentation solutions often utilize millions of parameters to extract high-level image features and neglect the incorporation of prior domain knowledge, which consequently consumes substantial computational resources and increases the risk of overfitting, especially when limited medical image samples are available for training. To address these challenges, we proposed a novel memory-efficient strategy that exploits graph structures derived from the images. Specifically, we introduced a lightweight superpixel-based graph neural network (GNN) and broke new ground by introducing superpixel metric learning to segment nucleus and cytoplasm. Remarkably, our proposed segmentation model superpixel metric graph neural network (SMGNN) achieved state of the art segmentation performance while utilizing at most 10000 \times less than the parameters compared to existing approaches. The subsequent segmentation-based cell type classification processes showed satisfactory results that such automatic recognizing algorithms are accurate and efficient to execeute in hematological laboratories. Our code is publicly available at https://github.com/jyh6681/SPXL-GNN.
@article{jiang2023automatic, title = {Automatic Recognition of White Blood Cell Images with Memory Efficient Superpixel Metric GNN: SMGNN}, author = {Jiang, Yuanhong and Shen, Yiqing and Wang, Yu Guang and Ding, Qiaoqiao}, journal = {Mathematical Biosciences and Engineering}, volume = {21}, number = {2}, pages = {2163--2188}, year = {2024}, publisher = {American Institute of Mathematical Sciences}, } - Journal
NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems
SIAM Journal on Imaging Sciences, 2024Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (normalizing flow-based unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pretrained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and nonasymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems.
@article{cai2024nf, title = {NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems}, author = {Cai, Ziruo and Tang, Junqi and Mukherjee, Subhadip and Li, Jinglai and Sch{\"o}nlieb, Carola-Bibiane and Zhang, Xiaoqun}, journal = {SIAM Journal on Imaging Sciences}, volume = {17}, number = {2}, pages = {10--1137}, year = {2024}, } - Journal
On the Convergence of Continuous and Discrete Unbalanced Optimal Transport Models for 1-Wasserstein Distance
SIAM Journal on Numerical Analysis, 2024We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The Γ-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter Γgoes to infinity. The discretization of the problem is further shown to be asymptotic preserving regarding the same limit, which ensures that a numerical method can be applied uniformly and the solutions converge to the one of the OT problem automatically. Particularly, there exists a critical value, which is independent of the mesh size, such that the discrete problem reduces to the discrete OT problem for Γbeing larger than this critical value. The discrete problem is solved by a convergent primal-dual hybrid algorithm and the iterates for UOT are also shown to converge to that for OT. Finally, numerical experiments on shape deformation and partial color transfer are implemented to validate the theoretical convergence and the proposed numerical algorithm.
@article{xiong2024convergence, title = {On the Convergence of Continuous and Discrete Unbalanced Optimal Transport Models for 1-Wasserstein Distance}, author = {Xiong, Zhe and Li, Lei and Zhu, Ya-Nan and Zhang, Xiaoqun}, journal = {SIAM Journal on Numerical Analysis}, volume = {62}, number = {2}, pages = {749--774}, year = {2024}, publisher = {SIAM}, } - Journal
Vision Graph U-Net: Geometric Learning Enhanced Encoder for Medical Image Segmentation and Restoration
Inverse Problems and Imaging, 2024Convolutional neural networks (CNNs) are known for their powerful feature extraction ability, and have achieved great success in a variety of image processing tasks. However, convolution filters only extract local features and neglect long-range self-similarity information, which is the vital prior information commonly existing in image data. To this end, we put forward a new backbone neural network: vision graph U-Net (VGU-Net), which is the first model to construct multi-scale graph structures through the hierarchical down-sampling layers of the U-Net architecture. The graph structure is constructed by the self-attention mechanism. By replacing CNNs in the bottleneck layer and skip connection layers with the graph convolution networks (GCNs), the multi-scale graph structure visualization allows an interpretation of long-range interactions. We extend the VGU-Net backbone model for the widely considered compressed sensing MR image reconstruction task and propose a knowledge-driven deep unrolling scheme based on the half-quadratic splitting algorithm, which combines the interpretability of knowledge-driven model with the versatility of data-driven deep learning method to achieve remarkable reconstruction results. Moreover, we verify the segmentation ability of the VGU-Net backbone model on the multi-modality brain tumor segmentation dataset and white blood cell image segmentation dataset, and both achieve state-of-the-art performance. The code is publicly available at https://github.com/jyh6681/VGU-Net.
@article{jiang2024vision, title = {Vision Graph U-Net: Geometric Learning Enhanced Encoder for Medical Image Segmentation and Restoration}, author = {Jiang, Yuanhong and Ding, Qiaoqiao and Wang, Yu Guang and Lio, Pietro and Zhang, Xiaoqun}, journal = {Inverse Problems and Imaging}, volume = {18}, number = {3}, pages = {672--689}, year = {2024}, publisher = {Inverse Problems and Imaging}, } - Journal
Approximate Primal-Dual Fixed-Point Based Langevin Algorithms for Non-Smooth Convex Potentials
Communications in Mathematical Sciences, 2024The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for the standard Langevin algorithms, as they require to evaluate the gradient of the energy function in each iteration. To this end, a popular remedy is to utilize the proximity operator, and as a result one needs to solve a proximity subproblem in each iteration. The conventional practice is to solve the subproblems accurately, which can be exceedingly expensive, as the subproblem needs to be solved in each iteration. We propose an approximate primal-dual fixed-point algorithm for solving the subproblem, which only seeks an approximate solution of the subproblem and therefore reduces the computational cost considerably. We provide theoretical analysis of the proposed method and also demonstrate its performance with numerical examples.
@article{cai2023approximate, title = {Approximate Primal-Dual Fixed-Point Based Langevin Algorithms for Non-Smooth Convex Potentials}, author = {Cai, Ziruo and Li, Jinglai and Zhang, Xiaoqun}, journal = {Communications in Mathematical Sciences}, volume = {22}, number = {3}, pages = {655--684}, publisher = {International Press of Boston}, year = {2024}, } - Journal
Large Language Models as Surrogate Models in Evolutionary Algorithms: A Preliminary Study
Swarm and Evolutionary Computation, 2024Large Language Models (LLMs) have achieved significant progress across various fields and have exhibited strong potential in evolutionary computation, such as generating new solutions and automating algorithm design. Surrogate-assisted selection is a core step in evolutionary algorithms to solve expensive optimization problems by reducing the number of real evaluations. Traditionally, this has relied on conventional machine learning methods, leveraging historical evaluated evaluations to predict the performance of new solutions. In this work, we propose a novel surrogate model based purely on LLM inference capabilities, eliminating the need for training. Specifically, we formulate model-assisted selection as a classification and regression problem, utilizing LLMs to directly evaluate the quality of new solutions based on historical data. This involves predicting whether a solution is good or bad, or approximating its value. This approach is then integrated into evolutionary algorithms, termed LLM-assisted EA (LAEA). Detailed experiments compared the visualization results of 2D data from 9 mainstream LLMs, as well as their performance on optimization problems. The experimental results demonstrate that LLMs have significant potential as surrogate models in evolutionary computation, achieving performance comparable to traditional surrogate models only using inference. This work offers new insights into the application of LLMs in evolutionary computation. Code is available at: https://github.com/hhyqhh/LAEA.git
@article{hao2024llm, title = {Large Language Models as Surrogate Models in Evolutionary Algorithms: A Preliminary Study}, author = {Hao, Hao and Zhang, Xiaoqun and Zhou, Aimin}, journal = {Swarm and Evolutionary Computation}, volume = {91}, pages = {101741}, year = {2024}, publisher = {Elsevier}, } - Journal
Proton ARC Based LATTICE Radiation Therapy: Feasibility Study, Energy Layer Optimization and LET Optimization
Physics in Medicine & Biology, 2024Objective. LATTICE, a spatially fractionated radiation therapy (SFRT) modality, is a 3D generalization of GRID and delivers highly modulated peak-valley spatial dose distribution to tumor targets, characterized by peak-to-valley dose ratio (PVDR). Proton LATTICE is highly desirable, because of the potential synergy of the benefit from protons compared to photons, and the benefit from LATTICE compared to GRID. Proton LATTICE using standard proton RT via intensity modulated proton therapy (IMPT) (with a few beam angles) can be problematic with poor target dose coverage and high dose spill to organs-at-risk (OAR). This work will develop novel proton LATTICE method via proton ARC (with many beam angles) to overcome these challenges in target coverage and OAR sparing, with optimized delivery efficiency via energy layer optimization and optimized biological dose distribution via linear energy transfer (LET) optimization, to enable the clinical use of proton LATTICE. Approach. ARC based proton LATTICE is formulated and solved with energy layer optimization, during which plan quality and delivery efficiency are jointly optimized. In particular, the number of energy jumps (NEJ) is explicitly modelled and minimized during plan optimization for improving delivery efficiency, while target dose conformality and OAR dose objectives are optimized. The plan deliverability is ensured by considering the minimum-monitor-unit (MMU) constraint, and the plan robustness is accounted for using robust optimization. The biological dose is optimized via LET optimization. The optimization solution algorithm utilizes iterative convex relaxation method to handle the dose-volume constraint and the MMU constraint, with spot-weight optimization subproblems solved by proximal descent method. Main results. ARC based proton LATTCE substantially improved plan quality from IMPT based proton LATTICE, such as (1) improved conformity index (CI) from 0.47 to 0.81 for the valley target dose and from 0.62 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.68 Gy to 0.44 Gy (a 12% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 4.15 to 4.28 in the lung case. Moreover, energy layer optimization improved plan delivery efficiency for ARC based proton LATTICE, such as (1) reduced NEJ from 71 to 56 and (2) reduction of energy layer switching time by 65% and plan delivery time by 52% in the lung case. The biological target and OAR dose distributions were further enhanced via LET optimization. On the other hand, proton ARC LATTCE also substantially improved plan quality from VMAT LATTICE, such as (1) improved CI from 0.45 to 0.81 for the valley target dose and from 0.63 to 0.97 for the peak target dose, (2) reduced esophagus dose from 0.59 Gy to 0.38 Gy (a 10.5% reduction with respect to 2 Gy valley prescription dose) and (3) improved PVDR from 3.88 to 4.28 in the lung case. Significance. The feasibility of high-plan-quality proton LATTICE is demonstrated via proton ARC with substantially improved target dose coverage and OAR sparing compared to IMPT, while the plan delivery efficiency for ARC based proton LATTICE can be optimized using energy layer optimization.
@article{zhu2024proton, title = {Proton ARC Based LATTICE Radiation Therapy: Feasibility Study, Energy Layer Optimization and LET Optimization}, author = {Zhu, Ya-Nan and Zhang, Weijie and Setianegara, Jufri and Lin, Yuting and Traneus, Erik and Long, Yong and Zhang, Xiaoqun and Badkul, Rajeev and Akhavan, David and Wang, Fen and Chen, Ronald C. and Gao, Hao}, journal = {Physics in Medicine \& Biology}, volume = {69}, number = {21}, pages = {215027}, year = {2024}, publisher = {IOP Publishing}, } - Preprint
Bi-Modality Medical Images Synthesis by a Bi-Directional Discrete Process Matching Method
OpenReview preprint, 2024Recently, medical image synthesis gains more and more popularity, along with the rapid development of generative models. Medical image synthesis aims to generate an unacquired image modality, often from other observed data modalities. Synthesized images can be used for clinical diagnostic assistance, data augmentation for model training and validation or image quality improving. In the meanwhile, the flow-based models are among the successful generative models for the ability of generating realistic and high-quality synthetic images. However, most flow-based models require to calculate flow ordinary different equation (ODE) evolution steps in synthesis process, for which the performances are significantly limited by heavy computation time due to a large number of time iterations. In this paper, we propose a novel flow-based model, namely bi-directional Discrete Process Matching (Bi-DPM) to accomplish the bi-modality image synthesis tasks. Different to other flow matching based models, we propose to utilize both forward and backward ODE flows and enhance the consistency on the intermediate images over a few discrete time steps, resulting in a synthesis process maintaining high-quality generations for both modalities under the guidance of paired data. Our experiments on three datasets of MRI T1/T2 and CT/MRI demonstrate that Bi-DPM outperforms other state-of-the-art flow-based methods for bi-modality image synthesis, delivering higher image quality with accurate anatomical regions.
@article{xiong2024bimodality, title = {Bi-Modality Medical Images Synthesis by a Bi-Directional Discrete Process Matching Method}, author = {Xiong, Zhe and Ding, Qiaoqiao and Zhang, Xiaoqun}, journal = {OpenReview preprint}, year = {2024}, } - Conference
Model Uncertainty in Evolutionary Optimization and Bayesian Optimization: A Comparative Analysis
In 2024 IEEE Congress on Evolutionary Computation (CEC), 2024Black-box optimization problems, which are common in many real-world applications, require optimization through input-output interactions without access to internal workings. This often leads to significant computational resources being consumed for simulations. Bayesian Optimization (BO) and Surrogate-Assisted Evolutionary Algorithm (SAEA) are two widely used gradient-free optimization techniques employed to address such challenges. Both approaches follow a similar iterative procedure that relies on surrogate models to guide the search process. This paper aims to elucidate the similarities and differences in the utilization of model uncertainty between these two methods, as well as the impact of model inaccuracies on algorithmic performance. A novel model-assisted strategy is introduced, which utilizes unevaluated solutions to generate offspring, leveraging the population-based search capabilities of evolutionary algorithm to enhance the effectiveness of model-assisted optimization. Experimental results demonstrate that the proposed approach outperforms mainstream Bayesian optimization algorithms in terms of accuracy and efficiency.
@inproceedings{hao2024model, title = {Model Uncertainty in Evolutionary Optimization and Bayesian Optimization: A Comparative Analysis}, author = {Hao, Hao and Zhang, Xiaoqun and Zhou, Aimin}, booktitle = {2024 IEEE Congress on Evolutionary Computation (CEC)}, pages = {1--9}, year = {2024}, } - Journal
Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization
Science China Information Sciences, 2024Surrogate-assisted evolutionary algorithms (SAEAs) hold significant importance in resolving expensive optimization problems. Extensive efforts have been devoted to improving the efficiency of SAEAs through the development of proficient model-assisted solution selection methods, which, however, first requires generating high-quality solutions. The fundamental paradigm of evaluating a limited number of solutions in each generation within SAEAs reduces the variance of adjacent populations, thereby affecting the quality of offspring solutions. This is a frequently encountered issue yet receives little attention. To address the issue, this paper presents a framework using unevaluated solutions to enhance the efficiency of SAEAs. The surrogate model is employed to identify high-quality solutions for the direct generation of new solutions without evaluation. To ensure dependable selection, we have introduced two tailored relation models to select the optimal solution and the unevaluated population. A comprehensive experimental analysis is performed on two test suites, which showcases the superiority of the relation model over regression and classification models in the solution selection phase. Furthermore, the surrogate-selected unevaluated solutions with high potential have been shown to enhance the efficiency of the algorithm significantly.
@article{hao2024enhancing, title = {Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization}, author = {Hao, Hao and Zhang, Xiaoqun and Zhou, Aimin}, journal = {Science China Information Sciences}, volume = {67}, number = {2}, pages = {120103}, year = {2024}, publisher = {Science China Press}, }
2023
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A Distance Function Based Cascaded Neural Network for Accurate Polyps Segmentation and Classification
Inverse Problems and Imaging, 2023In clinical practice, accurate locating and measuring the size of polyps in general is a difficult task. In this work, based on the position constraint between the primary organ and polyps boundary, we propose a U-Net based cascaded neural network for the joint segmentation of the organ of interest and the polyps. The position constraint is enforced by considering a narrow-band distance function and complimentary dice function in the loss function. Through a series of comparisons and ablation study, we evaluate the performance of our proposed cascaded network architecture and the additional loss functions using an in-house dataset for gallbladder polyps segmentation and classification. Numerical results indicate that the proposed method achieves a significant improvement over conventional U-Net, U-Net++, etc.. Lastly, the pathological type classification based on the segmented polys shows 30% higher accuracy compared to those conventional ResNet based results.
@article{jiang2023distance, title = {A Distance Function Based Cascaded Neural Network for Accurate Polyps Segmentation and Classification}, author = {Jiang, Yuanhong and Liang, Jingwei and Xiong, Weiqi and Li, Qiwei and Zhang, Yijue and Chen, Tao and Zhang, Xiaoqun}, journal = {Inverse Problems and Imaging}, volume = {17}, number = {3}, pages = {646--659}, year = {2023}, publisher = {Inverse Problems and Imaging}, } - Conference
Robust Graph Representation Learning for Local Corruption Recovery
In Proceedings of the ACM Web Conference (WWW), 2023The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.
@inproceedings{zhou2023robust, title = {Robust Graph Representation Learning for Local Corruption Recovery}, author = {Zhou, Bingxin and Jiang, Yuanhong and Wang, Yuguang and Liang, Jingwei and Gao, Junbin and Pan, Shirui and Zhang, Xiaoqun}, booktitle = {Proceedings of the ACM Web Conference (WWW)}, pages = {438--448}, year = {2023}, } - Journal
The Prognostic Value of Splenic Abnormalities in Pretreatment 18F-FDG PET/CT in Patients with Complete Response Diffuse Large B-Cell Lymphoma
Clinical Radiology, 2023AIM To investigate whether spleen imaging characteristics of baseline 2-[18F]-fluoro-2-deoxy-d-glucose (18F-FDG) positron-emission tomography (PET)/computed tomography (CT) can help to predict the clinical outcome in complete response (CR) diffuse large B-cell lymphoma (DLBCL). MATERIALS AND METHODS Three hundred and six patients with DLBCL were enrolled in the study and divided into recurrence and non-recurrence groups. The splenic abnormalities were compared using the chi-square test and quantitative indexes were compared using the t-test. The Cox proportional hazard regression model was used for univariate and multivariate analysis. Kaplan-Meier curves and log-rank tests were used to compare progression-free survival (PFS). Propensity score matching (PSM) was used to match patients with and without splenic abnormalities according to age, gender, and initial Ann Arbor stage at a 1:2 ratio (52:104); then the recurrence and PFS results were compared again. RESULTS Age, international prognostic index (IPI), stage, splenomegaly, and focal splenic lesions were significantly different between the recurrence and non-recurrence groups. IPI, stage, baseline spleen mean standard uptake value (SUVmean)/liver SUVmean, splenomegaly, and focal lesions were selected by Cox single-factor analysis, and only focal lesions showed a statistical difference in terms of Cox multivariate analysis (p=0.022, hazard ratio [HR]: 2.843). After PSM, focal splenic lesions (n=20) were still statistically different (p=0.003) between the recurrence and non-recurrence groups, and this played an essential role in PFS forecasting (p=0.0004, HR: 3.767). CONCLUSION Focal splenic lesions were identified as an independent risk factor for the prognosis of DLBCL. Pretreatment splenomegaly and focal splenic lesions appeared to be related to the relapse and PFS of DLBCL patients. Focal splenic lesions still showed meaningful predictive value even with propensity matching.
@article{wang2023prognostic, title = {The Prognostic Value of Splenic Abnormalities in Pretreatment 18F-FDG PET/CT in Patients with Complete Response Diffuse Large B-Cell Lymphoma}, author = {Wang, S and Ju, H and Bai, Y and Wang, L and Ding, Q and Li, P and Jiang, X and Lin, X}, journal = {Clinical Radiology}, volume = {78}, number = {5}, pages = {375--380}, year = {2023}, publisher = {WB Saunders}, } - Journal
An Orthogonal Matching Pursuit Optimization Method for Solving Minimum-Monitor-Unit Problems: Applications to Proton IMPT, ARC and FLASH
Medical physics, 2023The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum‐MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher‐dose‐rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high‐dose‐rate‐induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve. This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state‐of‐the‐art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD). The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose‐volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non‐zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non‐zero spots localized via OMP will be adaptively added to or removed from the optimization objective. The new method via OMP is validated in comparison with ADMM, PGD and SCD for high‐dose‐rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. A new OMP‐based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD.
@article{zhu2023orthogonal, title = {An Orthogonal Matching Pursuit Optimization Method for Solving Minimum-Monitor-Unit Problems: Applications to Proton IMPT, ARC and FLASH}, author = {Zhu, Ya-Nan and Zhang, Xiaoqun and Lin, Yuting and Lominska, Chris and Gao, Hao}, journal = {Medical physics}, volume = {50}, number = {8}, pages = {4710--4720}, year = {2023}, } - Journal
Semi-Implicit Back Propagation
Journal of Nonlinear and Variational Analysis, 2023Deep neural network (DNN) has been attracting a great attention in various applications.Network training algorithms play essential roles for the effectiveness of DNN.Although stochastic gradient descent (SGD) and other explicit gradient-based methods are the most popular algorithms, there are still many challenges such as gradient vanishing and explosion occurring in training a complex and deep neural networks.Motivated by the idea of error back propagation (BP) and proximal point methods (PPM), we propose a semi-implicit back propagation method for neural network training.Similar to the BP, the update on the neurons are propagated in a backward fashion and the parameters are optimized with proximal mapping.The implicit update for both hidden neurons and parameters allows to choose large step size in the training algorithm.Theoretically, we demonstrate the convergence of the proposed method under some standard assumptions.The experiments on illustrative examples, and two real data sets: MNIST and CIFAR-10, demonstrate that the proposed semi-implicit BP algorithm leads to better performance in terms of both loss decreasing and training/test accuracy, with a detail comparison to SGD/Adam and a similar algorithm proximal back propagation (ProxBP).
@article{liu2020semi, title = {Semi-Implicit Back Propagation}, author = {Liu, Ren and Zhang, Xiaoqun}, journal = {Journal of Nonlinear and Variational Analysis}, volume = {7}, number = {4}, year = {2023}, } - Conference
AE-FLOW: Autoencoders with Normalizing Flows for Medical Images Anomaly Detection
In International Conference on Learning Representations (ICLR), 2023Anomaly detection from medical images is an important task for clinical screening and diagnosis. In general, a large dataset of normal images are available while only few abnormal images can be collected in clinical practice. By mimicking the diagnosis process of radiologists, we attempt to tackle this problem by learning a tractable distribution of normal images and identify anomalies by differentiating the original image and the reconstructed normal image. More specifically, we propose a normalizing flow-based autoencoder for an efficient and tractable representation of normal medical images. The anomaly score consists of the likelihood originated from the normalizing flow and the reconstruction error of the autoencoder, which allows to identify the abnormality and provide an interpretability at both image and pixel levels. Experimental evaluation on two medical images datasets showed that the proposed model outperformed the other approaches by a large margin, which validated the effectiveness and robustness of the proposed method.
@inproceedings{zhao2023ae, title = {AE-FLOW: Autoencoders with Normalizing Flows for Medical Images Anomaly Detection}, author = {Zhao, Yuzhong and Ding, Qiaoqiao and Zhang, Xiaoqun}, booktitle = {International Conference on Learning Representations (ICLR)}, year = {2023}, } - Journal
Sea-Net: Structure-Enhanced Attention Network for Limited-Angle CBCT Reconstruction of Clinical Projection Data
IEEE Transactions on Instrumentation and Measurement, 2023This work aims to improve limited-angle (LA) cone beam computed tomography (CBCT) by developing deep learning (DL) methods for real clinical CBCT projection data, which is the first feasibility study of clinical-projection-data-based LA-CBCT, to the best of our knowledge. In radiation therapy (RT), CBCT is routinely used as the on-board imaging modality for patient setup. Compared to diagnostic CT, CBCT has a long acquisition time, e.g., 60 seconds for a full 360° rotation, which is subject to the motion artifact. Therefore, the LA-CBCT, if achievable, is of the great interest for the purpose of RT, for its proportionally reduced scanning time in addition to the radiation dose. However, LA-CBCT suffers from severe wedge artifacts and image distortions. Targeting at real clinical projection data, we have explored various DL methods such as image/data/hybrid-domain methods and finally developed a so-called Structure-Enhanced Attention Network (SEA-Net) method that has the best image quality from clinical projection data among the DL methods we have implemented. Specifically, the proposed SEA-Net employs a specialized structure enhancement sub-network to promote texture preservation. Based on the observation that the distribution of wedge artifacts in reconstruction images is non-uniform, the spatial attention module is utilized to emphasize the relevant regions while ignores the irrelevant ones, which leads to more accurate texture restoration.
@article{hu2023sea, title = {Sea-Net: Structure-Enhanced Attention Network for Limited-Angle CBCT Reconstruction of Clinical Projection Data}, author = {Hu, Dianlin and Zhang, Yikun and Li, Wangyao and Zhang, Weijie and Reddy, Krishna and Ding, Qiaoqiao and Zhang, Xiaoqun and Chen, Yang and Gao, Hao}, journal = {IEEE Transactions on Instrumentation and Measurement}, year = {2023}, publisher = {IEEE}, } - Journal
Binary Quantized Network Training with Sharpness-Aware Minimization
Journal of Scientific Computing, 2023The quantized neural network is a common way to improve inference and memory efficiency for deep learning methods. However, it is challenging to solve this optimization problem with good generalization due to its high nonlinearity and nonconvexity. This paper proposes an algorithm to train one-bit quantization neural networks based on sharpness-aware minimization Foret et al. (Sharpness-aware minimization for efficiently improving generalization, 2021) with two types of gradient approximation. The idea is to improve the generalization by finding a local minimum of a flat landscape of both continuous and quantized neural network loss. The convergence theory is partially established under a one-bit quantization setting. Experiments on the CIFAR-10 Krizhevsky (Learning multiple layers of features from tiny images, 2009) and SVHN Netzer et al. (Reading digits in natural images with unsupervised feature learning, 2011) datasets show improvement in generalization with the proposed algorithm compared to other state-of-the-art quantized training methods.
@article{liu2023binary, title = {Binary Quantized Network Training with Sharpness-Aware Minimization}, author = {Liu, Ren and Bian, Fengmiao and Zhang, Xiaoqun}, journal = {Journal of Scientific Computing}, volume = {94}, number = {1}, pages = {16}, year = {2023}, publisher = {Springer US New York}, } - Conference
PET-3DFlow: A Normalizing Flow Based Method for 3D PET Anomaly Detection
In International Workshop on Computational Mathematics Modeling in Cancer Analysis (CMMCA), 2023Anomaly detection of Positron Emission Tomography (PET) are important tasks for clinical diagnosis and treatments. For 3D PET images, it is arduous for the annotations of lesions and the number of positive samples are generally very limited. Although there have been many work on deep learning based anomaly detection for medical images, most of them cannot be directly applied on 3D PET data. In this paper, from a set of normal PET data, we propose a tractable and efficient 3D normalizing flow based model, namely PET-3DFlow for anomaly detection and provide lesion localization for the reference of clinicians. The loss of In PET-3DFlow consists of the log-likelihood originated from the normalizing flow model and the reconstruction error of the autoencoder learned from the normal images. Experimental evaluation on 3D PET data showed that the proposed model outperformed the other approaches, which validated the effectiveness of our proposed PET anomaly detection method.
@inproceedings{xiong2023pet, title = {PET-3DFlow: A Normalizing Flow Based Method for 3D PET Anomaly Detection}, author = {Xiong, Zhe and Ding, Qiaoqiao and Zhao, Yuzhong and Zhang, Xiaoqun}, booktitle = {International Workshop on Computational Mathematics Modeling in Cancer Analysis (CMMCA)}, pages = {91--100}, year = {2023}, organization = {Springer}, }
2022
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Partial Smoothness and Constant Rank
SIAM Journal on Optimization, 2022In optimization, the notion of a partly smooth objective function is powerful for applications in algorithmic convergence and postoptimality analysis, and yet is complex to define. A shift in focus to the first-order optimality conditions reduces the concept to a simple constant-rank condition. In this view, partial smoothness extends to more general variational systems, encompassing in particular the saddlepoint operators underlying popular primal-dual splitting algorithms. For a broad class of semi-algebraic generalized equations, partial smoothness holds generically.
@article{lewis2022partial, title = {Partial Smoothness and Constant Rank}, author = {Lewis, Adrian S. and Liang, Jingwei and Tian, Tonghua}, journal = {SIAM Journal on Optimization}, volume = {32}, number = {1}, pages = {276--291}, year = {2022}, publisher = {SIAM}, } - Journal
Variable Screening for Sparse Online Regression
Journal of Computational and Graphical Statistics, 2022Sparsity-promoting regularizers are widely used to impose low-complexity structure (e.g., l1-norm for sparsity) to the regression coefficients of supervised learning. In the realm of deterministic optimization, the sequence generated by iterative algorithms (such as proximal gradient descent) exhibit “finite activity identification” property, that is, they can identify the low-complexity structure of the solution in a finite number of iterations. However, many online algorithms (such as proximal stochastic gradient descent) do not have this property owing to the vanishing step-size and nonvanishing variance. In this article, by combining with a screening rule, we show how to eliminate useless features of the iterates generated by online algorithms, and thereby enforce finite sparsity identification. One advantage of our scheme is that when combined with any convergent online algorithm, sparsity properties imposed by the regularizer can be exploited to improve computational efficiency. Numerically, significant acceleration can be obtained.
@article{liang2022variable, title = {Variable Screening for Sparse Online Regression}, author = {Liang, Jingwei and Poon, Clarice}, journal = {Journal of Computational and Graphical Statistics}, pages = {1--19}, year = {2022}, publisher = {Taylor \& Francis}, } - Journal
On Biased Stochastic Gradient Estimation
Journal of Machine Learning Research, 2022We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we present allows us to extend proximal support to biased algorithms, including SAG and SARAH, for the first time in the convex setting. We also use our framework to develop a new algorithm, Stochastic Average Recursive GradiEnt (SARGE), that achieves the oracle complexity lower-bound for non-convex, finite-sum objectives and requires strictly fewer calls to a stochastic gradient oracle per iteration than SVRG and SARAH. We support our theoretical results with numerical experiments that demonstrate the benefits of certain biased gradient estimators.
@article{driggs2022biased, title = {On Biased Stochastic Gradient Estimation}, author = {Driggs, Derek and Liang, Jingwei and Sch{\"o}nlieb, Carola-Bibiane}, journal = {Journal of Machine Learning Research}, volume = {23}, number = {24}, pages = {1--43}, year = {2022}, } - Journal
TFPNP: Tuning-Free Plug-And-Play Proximal Algorithms with Applications to Inverse Imaging Problems
Journal of Machine Learning Research, 2022Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical success has been obtained by PnP algorithms, especially for the ones that integrate deep learning-based denoisers. However, a key problem of PnP approaches is the need for manual parameter tweaking which is essential to obtain high-quality results across the high discrepancy in imaging conditions and varying scene content. In this work, we present a class of tuning-free PnP proximal algorithms that can determine parameters such as denoising strength, termination time, and other optimization-specific parameters automatically. A core part of our approach is a policy network for automated parameter search which can be effectively learned via a mixture of model-free and model-based deep reinforcement learning strategies. We demonstrate, through rigorous numerical and visual experiments, that the learned policy can customize parameters to different settings, and is often more efficient and effective than existing handcrafted criteria. Moreover, we discuss several practical considerations of PnP denoisers, which together with our learned policy yield state-of-the-art results. This advanced performance is prevalent on both linear and nonlinear exemplar inverse imaging problems, and in particular shows promising results on compressed sensing MRI, sparse-view CT, single-photon imaging, and phase retrieval.
@article{wei2022tfpnp, title = {TFPNP: Tuning-Free Plug-And-Play Proximal Algorithms with Applications to Inverse Imaging Problems}, author = {Wei, Kaixuan and Aviles-Rivero, Angelica and Liang, Jingwei and Fu, Ying and Huang, Hua and Sch{\"o}nlieb, Carola-Bibiane}, journal = {Journal of Machine Learning Research}, volume = {23}, number = {16}, pages = {1--48}, year = {2022}, } - Journal
Improving “Fast Iterative Shrinkage-Thresholding Algorithm”: Faster, Smarter, and Greedier
SIAM Journal on Scientific Computing, 2022The “fast iterative shrinkage-thresholding algorithm,” a.k.a. FISTA, is one of the most well known first-order optimization scheme in the literature, as it achieves the worst-case O(1/k^2) optimal convergence rate for objective function value. However, despite such an optimal theoretical convergence rate, in practice the (local) oscillatory behavior of FISTA often damps its efficiency. Over the past years, various efforts have been made in the literature to improve the practical performance of FISTA, such as monotone FISTA, restarting FISTA, and backtracking strategies. In this paper, we propose a simple yet effective modification to the original FISTA scheme which has two advantages: It allows us to (1) prove the convergence of generated sequence and (2) design a so-called lazy-start strategy which can be up to an order faster than the original scheme. Moreover, we propose novel adaptive and greedy strategies which further improve the practical performance. The advantages of the proposed schemes are tested through problems arising from inverse problems, machine learning, and signal/image processing.
@article{liang2022improving, title = {Improving “Fast Iterative Shrinkage-Thresholding Algorithm”: Faster, Smarter, and Greedier}, author = {Liang, Jingwei and Luo, Tao and Schönlieb, Carola-Bibiane}, journal = {SIAM Journal on Scientific Computing}, volume = {44}, number = {3}, pages = {A1069--A1091}, year = {2022}, publisher = {SIAM}, } - Journal
Nomogram Based on Clinical and Radiomics Data for Predicting Radiation-Induced Temporal Lobe Injury in Patients with Non-Metastatic Stage T4 Nasopharyngeal Carcinoma
Clinical Oncology, 2022AIMS To use pre-treatment magnetic resonance imaging-based radiomics data with clinical data to predict radiation-induced temporal lobe injury (RTLI) in nasopharyngeal carcinoma (NPC) patients with stage T4/N0-3/M0 within 5 years after radiotherapy. MATERIALS AND METHODS This study retrospectively examined 98 patients (198 temporal lobes) with stage T4/N0-3/M0 NPC. Participants were enrolled into a training cohort or a validation cohort in a ratio of 7:3. Radiomics features were extracted from pre-treatment magnetic resonance imaging that were T1-and T2-weighted. Spearman rank correlation, the t-test and the least absolute shrinkage and selection operator (LASSO) algorithm were used to select significant radiomics features; machine-learning models were used to generate radiomics signatures (Rad-Scores). Rad-Scores and clinical factors were integrated into a nomogram for prediction of RTLI. Nomogram discrimination was evaluated using receiver operating characteristic analysis and clinical benefits were evaluated using decision curve analysis. RESULTS Participants were enrolled into a training cohort (n = 139) or a validation cohort (n = 59). In total, 3568 radiomics features were initially extracted from T1-and T2-weighted images. Age, Dmax, D1cc and 16 stable radiomics features (six from T1-weighted and 10 from T2-weighted images) were identified as independent predictive factors. A greater Rad-Score was associated with a greater risk of RTLI. The nomogram showed good discrimination, with a C-index of 0.85 (95% confidence interval 0.79-0.92) in the training cohort and 0.82 (95% confidence interval 0.71-0.92) in the validation cohort. CONCLUSION We developed models for the prediction of RTLI in patients with stage T4/N0-3/M0 NPC using pre-treatment radiomics data and clinical data. Nomograms from these pre-treatment data improved the prediction of RTLI. These results may allow the selection of patients for earlier clinical interventions.
@article{bin2022nomogram, title = {Nomogram Based on Clinical and Radiomics Data for Predicting Radiation-Induced Temporal Lobe Injury in Patients with Non-Metastatic Stage T4 Nasopharyngeal Carcinoma}, author = {Bin, Xiang and Zhu, Chao hua and Tang, Yanyan and Li, Renyuan and Ding, Qiaoqiao and others}, journal = {Clinical Oncology}, year = {2022}, publisher = {Clinical Oncology}, } - Journal
Low-Rank and Framelet Based Sparsity Decomposition for Interventional MRI Reconstruction
IEEE Transactions on Biomedical Engineering, 2022OBJECTIVE: Interventional MRI (i-MRI) is crucial for MR image-guided therapy. Current image reconstruction methods for dynamic MR imaging are mostly retrospective that may not be suitable for real-time i-MRI. Therefore, an algorithm to reconstruct images without a temporal pattern as in dynamic imaging is needed for i-MRI. METHODS: We proposed a low-rank and sparsity (LS) decomposition algorithm with framelet transform to reconstruct the interventional feature with a high temporal resolution. Different from the existing LS-based algorithms, the spatial sparsity of both the low-rank and sparsity components was used. We also used a primal dual fixed point (PDFP) method for optimization of the objective function to avoid solving sub-problems. Intervention experiments with gelatin and brain phantoms were carried out for validation. RESULTS: The LS decomposition with framelet transform and PDFP could provide the best reconstruction performance compared with those without. Satisfying reconstruction results were obtained with only 10 radial spokes for a temporal resolution of 60 ms. CONCLUSION AND SIGNIFICANCE: The proposed method has the potential for i-MRI in many different application scenarios.
@article{he2022low, title = {Low-Rank and Framelet Based Sparsity Decomposition for Interventional MRI Reconstruction}, author = {He, Zhao and Zhu, Ya-Nan and Qiu, Suhao and Wang, Tao and Zhang, Chencheng and Sun, Bomin and Zhang, Xiaoqun and Feng, Yuan}, journal = {IEEE Transactions on Biomedical Engineering}, volume = {69}, number = {7}, pages = {2294--2304}, year = {2022}, publisher = {IEEE}, } - Journal
A Dataset-Free Deep Learning Method for Low-Dose CT Image Reconstruction
Inverse Problems, 2022Low-dose CT (LDCT) imaging attracted a considerable interest for the reduction of the object’s exposure to x-ray radiation. In recent years, supervised deep learning (DL) has been extensively studied for LDCT image reconstruction, which trains a network over a dataset containing many pairs of normal-dose and low-dose images. However, the challenge on collecting many such pairs in the clinical setup limits the application of supervised-learning-based methods for LDCT image reconstruction in practice. Aiming at addressing the challenges raised by the collection of a training dataset, this paper proposed an unsupervised DL method for LDCT image reconstruction, which does not require any external training data. The proposed method is built on a re-parametrization technique for Bayesian inference via a deep network with random weights, combined with additional total variational regularization. The experiments show that the proposed method noticeably outperforms existing dataset-free image reconstruction methods on the test data.
@article{ding2022dataset, title = {A Dataset-Free Deep Learning Method for Low-Dose CT Image Reconstruction}, author = {Ding, Qiaoqiao and Ji, Hui and Quan, Yuhui and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {38}, number = {10}, pages = {104003}, year = {2022}, publisher = {IOP Publishing}, } - Conference
MRI Reconstruction by Completing Under-Sampled K-Space Data with Learnable Fourier Interpolation
In International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), 2022Magnetic resonance imaging (MRI) acceleration is usually achieved by data undersampling, while reconstruction from undersampled data is a challenging ill-posed problem for data-missing and noisy measurements introduce various artifacts. In recent years, deep learning methods have been extensively studied for MRI reconstruction, and most of work treat the reconstruction problem as a denoising problem or replace the regularization subproblem with a deep neural network (DNN) in an optimization unrolling scheme. In this work, we proposed to directly complete the missing and corrupted k-space data by a specially designed interpolation deep neural networks combined with some convolution layers in both frequency and spatial domains. Specifically, for every missing and corrupted frequency, we use a K- nearest neighbors estimation with learnable weights. Then, two convolution neural networks (CNNs) are applied to regularize the data in both k-space and image space. The proposed DNN structures have clear interpretability for solving this undersampling problem. Extensive experiments on MRI reconstruction with diverse sampling patterns and ratios, under noiseless and noise settings demonstrate the accuracy of the proposed method compared to other learning based algorithms, while being computationally more efficient for both training and reconstruction processes.
@inproceedings{ding2022mri, title = {MRI Reconstruction by Completing Under-Sampled K-Space Data with Learnable Fourier Interpolation}, author = {Ding, Qiaoqiao and Zhang, Xiaoqun}, booktitle = {International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI)}, pages = {676--685}, year = {2022}, organization = {Springer Nature Switzerland Cham}, }
2021
- Journal
A Stochastic Alternating Direction Method of Multipliers for Non-Smooth and Non-Convex Optimization
Inverse Problems, 2021Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the performance of ADMM degrades significantly when the scale of optimization problems to solve becomes large. In this paper, we consider combining ADMM with a class of variance-reduced stochastic gradient estimators for solving large-scale non-convex and non-smooth optimization problems. Global convergence of the generated sequence is established under the additional assumption that the object function satisfies Kurdyka-Łojasiewicz property. Numerical experiments on graph-guided fused lasso and computed tomography are presented to demonstrate the performance of the proposed methods.
@article{bian2021stochastic, title = {A Stochastic Alternating Direction Method of Multipliers for Non-Smooth and Non-Convex Optimization}, author = {Bian, Fengmiao and Liang, Jingwei and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {37}, year = {2021}, publisher = {IOP Publishing}, } - Journal
A Stochastic Proximal Alternating Minimization for Nonsmooth and Nonconvex Optimization
SIAM Journal on Imaging Sciences, 2021In this work, we introduce a novel stochastic proximal alternating linearized minimization algorithm [J. Bolte, S. Sabach, and M. Teboulle, Math. Program., 146 (2014), pp. 459–494] for solving a class of nonsmooth and nonconvex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to the advances in data acquisition and computational capabilities. Motivated by the success of stochastic optimization methods, we propose a stochastic variant of proximal alternating linearized minimization. We provide global convergence guarantees, demonstrating that our proposed method with variance-reduced stochastic gradient estimators, such as SAGA [A. Defazio, F. Bach, and S. Lacoste-Julien, Advances in Neural Information Processing Systems, 2014, pp. 1646–1654] and SARAH [L. M. Nguyen, J. Liu, K. Scheinberg, and M. Takáĉ, Proceedings of the 34th International Conference on Machine Learning, PMLR 70, 2017, pp. 2613–2621], achieves state-of-the-art oracle complexities. We also demonstrate the efficacy of our algorithm via several numerical examples including sparse nonnegative matrix factorization, sparse principal component analysis, and blind image-deconvolution.
@article{driggs2021stochastic, title = {A Stochastic Proximal Alternating Minimization for Nonsmooth and Nonconvex Optimization}, author = {Driggs, Derek and Tang, Junqi and Liang, Jingwei and Davies, Mike and Schönlieb, Carola-Bibiane}, journal = {SIAM Journal on Imaging Sciences}, volume = {14}, number = {4}, pages = {1932--1970}, year = {2021}, publisher = {Society for Industrial and Applied Mathematics}, } - Preprint
An Adaptive Rank Continuation Algorithm for General Weighted Low-Rank Recovery
arXiv preprint arXiv:2101.00749, 2021This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the literature. Moreover, our model readily extends to the non-convex setting. Algorithm-wise, most first-order proximal algorithms in the literature for low-rank recoveries require computing singular value decomposition (SVD). As SVD does not scale appropriately with the dimension of the matrices, these algorithms become slower when the problem size becomes larger. By incorporating the variational formulation of the nuclear norm into the sub-problem of proximal gradient descent, we avoid computing SVD, which results in significant speed-up. Moreover, our algorithm preserves the rank identification property of nuclear norm [33] which further allows us to design a rank continuation scheme that asymptotically achieves the minimal iteration complexity. Numerical experiments on both toy examples and real-world problems, including structure from motion (SfM) and photometric stereo, background estimation, and matrix completion, demonstrate the superiority of our proposed algorithm.
@article{dutta2021adaptive, title = {An Adaptive Rank Continuation Algorithm for General Weighted Low-Rank Recovery}, author = {Dutta, Aritra and Liang, Jingwei and Li, Xin}, journal = {arXiv preprint arXiv:2101.00749}, year = {2021}, } - Journal
Deep Learning with Adaptive Hyper-Parameters for Low-Dose CT Image Reconstruction
IEEE Transactions on Computational Imaging, 2021Low-dose CT (LDCT) imaging is preferred in many applications to reduce the object’s exposure to X-ray radiation. In recent years, one promising approach to image reconstruction in LDCT is the so-called optimization-unrolling-based deep learning approach, which replaces pre-defined image prior by learnable adaptive prior in some model-based iterative image reconstruction scheme (MBIR). While it is known that setting appropriate hyper-parameters in MBIR is challenging yet important to the reconstruction quality, it does not receive enough attention in the development of deep learning methods. This paper proposed a deep learning method for LDCT reconstruction that unrolls a half-quadratic splitting scheme. The proposed method not only introduces learnable image prior built on framelet filter bank, but also learns a network that automatically adjusts the hyper-parameters to fit noise level and the data for processing. As a result, only one universal model needs to be trained in our method to process the data taken under different dose levels. Experimental evaluation on clinical patient dataset showed that the proposed method outperformed both conventional and deep-learning-based solutions by a large margin.
@article{ding2021deep, title = {Deep Learning with Adaptive Hyper-Parameters for Low-Dose CT Image Reconstruction}, author = {Ding, Qiaoqiao and Nan, Yuesong and Gao, Hao and Ji, Hui}, journal = {IEEE Transactions on Computational Imaging}, year = {2021}, } - Conference
Learnable Multi-Scale Fourier Interpolation for Sparse View CT Image Reconstruction
In Medical Image Computing and Computer Assisted Intervention (MICCAI), 2021Image reconstruction in sparse view CT is a challenging ill-posed inverse problem, which aims at reconstructing a high-quality image from few and noisy measurements. As a prominent tool in the recent development of CT reconstruction, deep neural network (DNN) is mostly used as a denoising post-process or a regularization sub-module in some optimization unrolling method. As the problem of CT reconstruction essentially is about how to convert discrete Fourier transform in polar coordinates to its counterpart in Cartesian coordinates, this paper proposed to directly learn an interpolation scheme, modeled by a multi-scale DNN, for predicting 2D Fourier coefficients in Cartesian coordinates from the available ones in polar coordinates. The experiments showed that, in comparison to existing DNN-based solutions, the proposed DNN-based Fourier interpolation method not only provided the state-of-the-art performance, but also is much more computationally efficient.
@inproceedings{ding2021learnable, title = {Learnable Multi-Scale Fourier Interpolation for Sparse View CT Image Reconstruction}, author = {Ding, Qiaoqiao and Ji, Hui and Gao, Hao and Zhang, Xiaoqun}, booktitle = {Medical Image Computing and Computer Assisted Intervention (MICCAI)}, pages = {286--295}, year = {2021}, organization = {Springer}, } - Journal
A Stochastic Variance Reduced Primal Dual Fixed Point Method for Linearly Constrained Separable Optimization
SIAM Journal on Imaging Sciences, 2021In this paper we combine the stochastic variance reduced gradient (SVRG) method [R. Johnson and T. Zhang, in Advances in Neural Information Processing Systems 26, 2013, pp. 315–323] with the primal dual fixed point method (PDFP) proposed in [P. Chen, J. Huang, and X. Zhang, Inverse Problems, 29 (2013)] to minimize a sum of two convex functions, one of which is linearly composite. This type of problems typically arise in sparse signal and image reconstruction. The proposed SVRG-PDFP can be seen as a generalization of Prox-SVRG [L. Xiao and T. Zhang, SIAM J. Optim., 24 (2014), pp. 2057–2075] originally designed for the minimization of a sum of two convex functions. Based on some standard assumptions, we propose two variants, one for strongly convex objective functions and the other for the general convex case. Convergence analysis shows that the convergence rate of SVRG-PDFP is \mathcalO(\frac1k) (here k is the iteration number) for the general convex objective function and linear for the strongly convex case. Numerical examples on machine learning and computerized tomography image reconstruction are provided to show the effectiveness of the algorithms.
@article{zhu2021stochastic, title = {A Stochastic Variance Reduced Primal Dual Fixed Point Method for Linearly Constrained Separable Optimization}, author = {Zhu, Ya-Nan and Zhang, Xiaoqun}, journal = {SIAM Journal on Imaging Sciences}, volume = {14}, number = {3}, pages = {1326--1353}, year = {2021}, publisher = {SIAM}, } - Journal
A Three-Operator Splitting Algorithm for Nonconvex Sparsity Regularization
SIAM Journal on Scientific Computing, 2021Sparsity regularization has been widely adopted in many fields, such as signal and image processing and machine learning. In this paper, we mainly consider nonconvex minimization problems involving three terms, for applications such as sparse signal recovery and low rank matrix recovery. We employ a three-operator splitting proposed by Davis and Yin [ Set-Valued Var. Anal., 25 (2017), pp. 829–858] (namely, DYS) to solve the resulting possibly nonconvex problems and develop the convergence theory for this three-operator splitting algorithm in the nonconvex case. We show that when the step size is chosen less than a computable threshold, the whole sequence converges to a stationary point. By defining a new decreasing energy function associated with the DYS method, we establish the global convergence of the whole sequence and a local convergence rate under an additional assumption that F, G, and H are semialgebraic. We also provide sufficient conditions for the boundedness of the generated sequence. Finally, some numerical experiments are conducted to compare the DYS algorithm with some classical efficient algorithms for sparse signal recovery and low rank matrix completion. The numerical results indicate that DYS outperforms the existing methods for these applications.
@article{bian2021three, title = {A Three-Operator Splitting Algorithm for Nonconvex Sparsity Regularization}, author = {Bian, Fengmiao and Zhang, Xiaoqun}, journal = {SIAM Journal on Scientific Computing}, volume = {43}, number = {4}, pages = {A2809--A2839}, year = {2021}, publisher = {SIAM}, } - Journal
A Parameterized Douglas–Rachford Splitting Algorithm for Nonconvex Optimization
Applied Mathematics and Computation, 2021In this paper, we study a parameterized Douglas-Rachford splitting method for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized Douglas-Rachford splitting method. We then apply the parameterized Douglas-Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas-Rachford splitting method compared with some other classical methods.
@article{bian2021parameterized, title = {A Parameterized Douglas--Rachford Splitting Algorithm for Nonconvex Optimization}, author = {Bian, Fengmiao and Zhang, Xiaoqun}, journal = {Applied Mathematics and Computation}, volume = {410}, pages = {126425}, year = {2021}, publisher = {Elsevier}, } - Journal
Image Fusion Network for Dual-Modal Restoration
Inverse Problems and Imaging, 2021In recent years multi-modal data processing methods have gained considerable research interest as technological advancements in imaging, computing, and data storage have made the collection of redundant, multi-modal data more commonplace. In this work we present an image restoration method tailored for scenarios where pre-existing, high-quality images from different modalities or contrasts are available in addition to the target image. Our method is based on a novel network architecture which combines the benefits of traditional multi-scale signal representation, such as wavelets, with more recent concepts from data fusion methods. Results from numerical simulations in which T1-weighted MRI images are used to restore noisy and undersampled T2-weighted images demonstrate that the proposed network successfully utilizes information from high-quality reference images to improve the restoration quality of the target image beyond that of existing popular methods.
@article{zhang2021image, title = {Image Fusion Network for Dual-Modal Restoration}, author = {Zhang, Ying and Ren, Xuhua and Clifford, Bryan Alexander and Wang, Qian and Zhang, Xiaoqun}, journal = {Inverse Problems and Imaging}, volume = {15}, number = {6}, pages = {1409--1419}, year = {2021}, publisher = {Inverse Problems and Imaging}, } - Journal
A Greedy Algorithm for Sparse Precision Matrix Approximation
Journal of Computational Mathematics, 2021Precision matrix estimation is an important problem in statistical data analysis. This paper proposes a sparse precision matrix estimation approach, based on CLIME estimator and an efficient algorithm GISS^ρ that was originally proposed for l_1 sparse signal recovery in compressed sensing. The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISS^ρ algorithm. Finally, numerical comparison of GISS^ρ with other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.
@article{lv2019greedy, title = {A Greedy Algorithm for Sparse Precision Matrix Approximation}, author = {Lv, Didi and Zhang, Xiaoqun}, journal = {Journal of Computational Mathematics}, volume = {39}, number = {5}, pages = {693--707}, publisher = {Global Science Press}, year = {2021}, }
2020
- Conference
Tuning-Free Plug-And-Play Proximal Algorithm for Inverse Imaging Problems
In International Conference on Machine Learning (ICML), 2020This paper received the Outstanding Paper Award from ICML2020.
Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters including the penalty parameter, the denoising strength and the terminal time. A key part of our approach is to develop a policy network for automatic search of parameters, which can be effectively learned via mixed model-free and model-based deep reinforcement learning. We demonstrate, through numerical and visual experiments, that the learned policy can customize different parameters for different states, and often more efficient and effective than existing handcrafted criteria. Moreover, we discuss the practical considerations of the plugged denoisers, which together with our learned policy yield state-of-the-art results. This is prevalent on both linear and nonlinear exemplary inverse imaging problems, and in particular, we show promising results on Compressed Sensing MRI and phase retrieval.
@inproceedings{wei2020tuning, title = {Tuning-Free Plug-And-Play Proximal Algorithm for Inverse Imaging Problems}, author = {Wei, Kaixuan and Aviles-Rivero, Angelica and Liang, Jingwei and Fu, Ying and Sch{\"o}nlieb, Carola-Bibiane and Huang, Hua}, booktitle = {International Conference on Machine Learning (ICML)}, pages = {10158--10169}, year = {2020}, organization = {PMLR}, } - Preprint
Geometry of First-Order Methods and Adaptive Acceleration
arXiv preprint arXiv:2003.03910, 2020First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we study a geometric property of first-order methods when applying to solve non-smooth optimization problems. With the tool of "partial smoothness", we design a framework to analyze the trajectory of the fixed-point sequence generated by first-order methods and show that locally, the fixed-point sequence settles onto a regular trajectory such as a straight line or a spiral. Based on this finding, we discuss the limitation of current widely used "inertial acceleration" technique, and propose a trajectory following adaptive acceleration algorithm. Global convergence is established for the proposed acceleration scheme based on the perturbation of fixed-point iteration. Locally, we first build connections between the acceleration scheme and the well-studied "vector extrapolation technique" in the field of numerical analysis, and then discuss local acceleration guarantees of the proposed acceleration scheme. Moreover, our result provides a geometric interpretation of these vector extrapolation techniques. Numerical experiments on various first-order methods are provided to demonstrate the advantage of the proposed adaptive acceleration scheme.
@article{poon2020geometry, title = {Geometry of First-Order Methods and Adaptive Acceleration}, author = {Poon, Clarice and Liang, Jingwei}, journal = {arXiv preprint arXiv:2003.03910}, year = {2020}, } - Journal
The Fun Is Finite: Douglas-Rachford and Sudoku Puzzle–Finite Termination and Local Linear Convergence
Journal of Applied and Numerical Optimization, 2020In recent years, the Douglas-Rachford splitting method has been shown to be effective at solving many non-convex optimization problems. In this paper we present a local convergence analysis for non-convex feasibility problems and show that both finite termination and local linear convergence are obtained. For a generalization of the Sudoku puzzle, we prove that the local linear rate of convergence of Douglas-Rachford is exactly $\frac\sqrt55 and independent of puzzle size. For the s$-queens problem we prove that Douglas-Rachford converges after a finite number of iterations. Numerical results on solving Sudoku puzzles and s-queens puzzles are provided to support our theoretical findings.
@article{tovey2020fun, title = {The Fun Is Finite: Douglas-Rachford and Sudoku Puzzle--Finite Termination and Local Linear Convergence}, author = {Tovey, Robert and Liang, Jingwei}, journal = {Journal of Applied and Numerical Optimization}, year = {2020}, } - Journal
Best Pair Formulation & Accelerated Scheme for Non-Convex Principal Component Pursuit
IEEE Transactions on Signal Processing, 2020Given two disjoint sets, the best pair problem aims to find a point in one set and another point in the other set with minimal distance between them. In this paper, we formulate the classical robust principal component analysis (RPCA) problem as a best pair problem and design an accelerated proximal gradient algorithm to solve it. We prove that the method enjoys global convergence with a local linear rate. Our extensive numerical experiments on both real and synthetic data sets suggest that our proposed algorithm outperforms relevant baseline algorithms in the literature.
@article{dutta2020best, title = {Best Pair Formulation \& Accelerated Scheme for Non-Convex Principal Component Pursuit}, author = {Dutta, Aritra and Hanzely, Filip and Liang, Jingwei and Richt{\'a}rik, Peter}, journal = {IEEE Transactions on Signal Processing}, year = {2020}, publisher = {IEEE}, } - Journal
Bayesian Inference and Uncertainty Quantification for Medical Image Reconstruction with Poisson Data
SIAM Journal on Imaging Sciences, 2020We provide a complete framework for performing infinite dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework applicable in practice. We first introduce a positivity-preserving reparametrization, and we prove that under the reparametrization and a hybrid prior, the posterior distribution is well-posed in the infinite dimensional setting. Second, we provide a dimension-independent Markov chain Monte Carlo algorithm, based on the preconditioned Crank–Nicolson Langevin method, in which we use a primal-dual scheme to compute the offset direction. Third, we give a method combining the model discrepancy method and maximum likelihood estimation to determine the regularization parameter in the hybrid prior. Finally we propose to use the obtained posterior distribution to detect artifacts in a recovered image. We provide an example to demonstrate the effectiveness of the proposed method.
@article{zhou2020bayesian, title = {Bayesian Inference and Uncertainty Quantification for Medical Image Reconstruction with Poisson Data}, author = {Zhou, Qingping and Yu, Tengchao and Zhang, Xiaoqun and Li, Jinglai}, journal = {SIAM Journal on Imaging Sciences}, volume = {13}, number = {1}, pages = {29--52}, year = {2020}, publisher = {Society for Industrial and Applied Mathematics}, } - Journal
An Edge Driven Wavelet Frame Model for Image Restoration
Applied and Computational Harmonic Analysis, 2020Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.
@article{choi2020edge, title = {An Edge Driven Wavelet Frame Model for Image Restoration}, author = {Choi, Jae Kyu and Dong, Bin and Zhang, Xiaoqun}, journal = {Applied and Computational Harmonic Analysis}, volume = {48}, number = {3}, pages = {993--1029}, year = {2020}, publisher = {Academic Press}, } - Journal
Computer-Aided Diagnosis of Gallbladder Polyps Based on High Resolution Ultrasonography
Computer methods and programs in biomedicine, 2020BACKGROUND AND OBJECTIVE Gallbladder polyp is a common disease with an overall population prevalence between 4 and 7%. It can be classified as neoplastic and non-neoplastic lesions. Surgical treatment is necessary for neoplastic polyps. Due to its easy accessibility and nonradioactive, ultrasonography is the mostly used preoperative diagnosis tool for gallbladder polyps. However, human image analysis depends greatly on levels of experience, which results in many overtreatment cases and undertreatment cases in clinics. METHODS In this study, we proposed an ultrasound image segmentation algorithm, combined with principal components analysis (PCA) and AdaBoost algorithms to construct a computer-aided diagnosis system for the differentiate diagnosis of neoplastic and non-neoplastic gallbladder polyps. RESULTS The proposed segmentation method achieved a high accuracy of 95% for outlining the gallbladder region. The accuracy, sensitivity, specificity for the proposed computer-aided diagnosis system based on the segmented images are 87.54%, 86.52% and 89.40%, compared to 69.05%, 67.86% and 70.17% with convolutional neural network. The diagnosis result is also slightly higher than the human eyes of sonologists (86.22%, 85.19% and 89.18% as an average of four sonologists), while with a much faster diagnosis speed (0.02s vs 3s). CONCLUSIONS We proposed an efficient ultrasound image segmentation approach and a reliable system of automatic diagonals of neoplastic and non-neoplastic gallbladder polyps. The results show that the diagnosis accuracy is competitive to the expert sonologists while requires much less diagnosis time.
@article{chen2020computer, title = {Computer-Aided Diagnosis of Gallbladder Polyps Based on High Resolution Ultrasonography}, author = {Chen, Tao and Tu, Shaoxiong and Wang, Haolu and Liu, Xuesong and Li, Fenghua and Jin, Wang and Liang, Xiaowen and Zhang, Xiaoqun and Wang, Jian}, journal = {Computer methods and programs in biomedicine}, volume = {185}, pages = {105118}, year = {2020}, publisher = {Elsevier}, } - Journal
Stochastic Primal Dual Fixed Point Method for Composite Optimization
Journal of Scientific Computing, 2020In this paper we propose a stochastic primal dual fixed point method for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method proposed in Chen et al. (Inverse Probl 29:025011, 2013) that does not require subproblem solving. Under some mild condition, the convergence is established based on two sets of assumptions: bounded and unbounded gradients and the convergence rate of the expected error of iterate is of the order \mathcal O(k^-α) where k is iteration number and α∈(0,1] . Finally, numerical examples on graphic Lasso and logistic regressions are given to demonstrate the effectiveness of the proposed algorithm.
@article{zhu2020stochastic, title = {Stochastic Primal Dual Fixed Point Method for Composite Optimization}, author = {Zhu, Ya-Nan and Zhang, Xiaoqun}, journal = {Journal of Scientific Computing}, volume = {84}, number = {1}, pages = {16}, year = {2020}, publisher = {Springer US New York}, } - Journal
Nonlocal TV-Gaussian Prior for Bayesian Inverse Problems with Applications to Limited CT Reconstruction.
Inverse Problems & Imaging, 2020Bayesian inference methods have been widely applied in inverse problems due to the ability of uncertainty characterization of the estimation. The prior distribution of the unknown plays an essential role in the Bayesian inference, and a good prior distribution can significantly improve the inference results. In this paper, we propose a hybrid prior distribution on combining the nonlocal total variation regularization (NLTV) and the Gaussian distribution, namely NLTG prior. The advantage of this hybrid prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the hybrid prior. We apply the proposed prior to limited tomography reconstruction problem that is difficult due to severe data missing. Both maximum a posteriori and conditional mean estimates are computed through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior.
@article{lv2020nonlocal, title = {Nonlocal TV-Gaussian Prior for Bayesian Inverse Problems with Applications to Limited CT Reconstruction.}, author = {Lv, Didi and Zhou, Qingping and Choi, Jae Kyu and Li, Jinglai and Zhang, Xiaoqun}, journal = {Inverse Problems \& Imaging}, volume = {14}, number = {1}, year = {2020}, } - Journal
Low-Dose CT with Deep Learning Regularization via Proximal Forward–Backward Splitting
Physics in Medicine & Biology, 2020Low-dose x-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops new image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on the unrolling of a proximal forward–backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast to PFBS-IR, which utilizes standard data fidelity updates via an iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse the analytical reconstruction (AR) and IR methods in a synergistic way, i.e. fused analytical and iterative reconstruction (AIR). The results suggest that the DL-regularized methods (PFBS-IR and PFBS-AIR) provide better reconstruction quality compared to conventional methods (AR or IR). In addition, owing to the AIR, PFBS-AIR noticeably outperformed PFBS-IR and another DL-based postprocessing method, FBPConvNet.
@article{ding2020low, title = {Low-Dose CT with Deep Learning Regularization via Proximal Forward--Backward Splitting}, author = {Ding, Qiaoqiao and Chen, Gaoyu and Zhang, Xiaoqun and Huang, Qiu and Ji, Hui and Gao, Hao}, journal = {Physics in Medicine \& Biology}, volume = {65}, number = {12}, pages = {125009}, year = {2020}, publisher = {IOP Publishing}, } - Journal
AirNet: Fused Analytical and Iterative Reconstruction with Deep Neural Network Regularization for Sparse-Data CT
Medical physics, 2020Sparse‐data computed tomography (CT) frequently occurs, such as breast tomosynthesis, C‐arm CT, on‐board four‐dimensional cone‐beam CT (4D CBCT), and industrial CT. However, sparse‐data image reconstruction remains challenging due to highly undersampled data. This work develops a data‐driven image reconstruction method for sparse‐data CT using deep neural networks (DNN). The new method so‐called AirNet is designed to incorporate the benefits from analytical reconstruction method (AR), iterative reconstruction method (IR), and DNN. It is built upon fused analytical and iterative reconstruction (AIR) that synergizes AR and IR via the optimization framework of modified proximal forward‐backward splitting (PFBS). By unrolling PFBS into IR updates of CT data fidelity and DNN regularization with residual learning, AirNet utilizes AR such as FBP during the data fidelity, introduces dense connectivity into DNN regularization, and learns PFBS coefficients and DNN parameters that minimize the loss function during the training stage; and then AirNet with trained parameters can be used for end‐to‐end image reconstruction. A CT atlas of 100 prostate scans was used to validate the AirNet in comparison with state‐of‐art DNN‐based postprocessing and image reconstruction methods. The validation loss in AirNet had the fastest decreasing rate, owing to inherited fast convergence from AIR. AirNet was robust to noise in projection data and content differences between the training set and the images to be reconstructed. The impact of image quality on radiotherapy treatment planning was evaluated for both photon and proton therapy, and AirNet achieved the best treatment plan quality, especially for proton therapy. For example, with limited‐angle data, the maximal target dose for AirNet was 109.5% in comparison with the ground truth 109.1%, while it was significantly elevated to 115.1% and 128.1% for FBPConvNet and LEARN, respectively. A new image reconstruction AirNet is developed for sparse‐data CT image reconstruction. AirNet achieved the best image reconstruction quality both visually and quantitatively among all methods under comparison for all sparse‐data scenarios (sparse‐view and limited‐angle), and provided the best photon and proton treatment plan quality based on sparse‐data CT.
@article{chen2020airnet, title = {AirNet: Fused Analytical and Iterative Reconstruction with Deep Neural Network Regularization for Sparse-Data CT}, author = {Chen, Gaoyu and Hong, Xiang and Ding, Qiaoqiao and Zhang, Yi and Chen, Hu and Fu, Shujun and Zhao, Yunsong and Zhang, Xiaoqun and Ji, Hui and Wang, Ge and others}, journal = {Medical physics}, volume = {47}, number = {7}, pages = {2916--2930}, year = {2020}, publisher = {Wiley Online Library}, } - Journal
Variational Bimodal Image Fusion with Data-Driven Tight Frame
Information Fusion, 2020The purpose of multimodal image fusion is to combine information from different modal images of the same investigated object and create an image that is suitable for human vision and subsequent image processing. This paper proposes a three-step method for bimodal image fusion. A tight frame system is first adaptively learned from bimodal images for capturing source images features as much as possible. Further, a fused coefficient set is constructed by integrating the frame coefficients from both modalities. Finally, a variational model is designed to reconstruct a fused image based on the fused coefficients, and the intensity information of those smooth regions. The alternating iteration scheme and alternating direction method of multipliers are used to solve the resulted variational problems. Numerical experiments on multimodal medical image fusion and multifocused natural image fusion indicate that the proposed approach outperforms some existing methods.
@article{zhang2020variational, title = {Variational Bimodal Image Fusion with Data-Driven Tight Frame}, author = {Zhang, Ying and Zhang, Xiaoqun}, journal = {Information Fusion}, volume = {55}, pages = {164--172}, year = {2020}, publisher = {Elsevier}, }
2019
- Conference
Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration
In Advances in Neural Information Processing Systems (NeurIPS), 2019Oral presentation
This paper was presented as an oral presentation at NeurIPS2019.
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to improve the performance of the method, such as the inertial technique. By studying the geometric properties of ADMM, we discuss the limitations of current inertial accelerated ADMM and then present and analyze an adaptive acceleration scheme for the method. Numerical experiments on problems arising from image processing, statistics and machine learning demonstrate the advantages of the proposed acceleration approach.
@inproceedings{poon2019trajectory, title = {Trajectory of Alternating Direction Method of Multipliers and Adaptive Acceleration}, author = {Poon, Clarice and Liang, Jingwei}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, pages = {7355--7363}, year = {2019}, } - Journal
Convergence Rates of Forward–Douglas–Rachford Splitting Method
Journal of Optimization Theory and Applications, 2019Over the past decades, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward-Douglas-Rachford splitting method and study both global and local convergence rates of this method. For the global rate, we establish a sublinear convergence rate in terms of a Bregman divergence suitably designed for the objective function. Moreover, when specializing to the Forward-Backward splitting, we prove a stronger convergence rate result for the objective function value. Then locally, based on the assumption that the non-smooth part of the optimization problem is partly smooth, we establish local linear convergence of the method. More precisely, we show that the sequence generated by Forward-Douglas-Rachford first (i) identifies a smooth manifold in a finite number of iteration and then (ii) enters a local linear convergence regime, which is for instance characterized in terms of the structure of the underlying active smooth manifold. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from applicative fields including, for instance, signal/image processing, inverse problems and machine learning.
@article{molinari2019convergence, title = {Convergence Rates of Forward--Douglas--Rachford Splitting Method}, author = {Molinari, Cesare and Liang, Jingwei and Fadili, Jalal}, journal = {Journal of Optimization Theory and Applications}, pages = {1--34}, year = {2019}, publisher = {Springer US}, } - Journal
A New Proximal Iterative Hard Thresholding Method with Extrapolation for L0 Minimization
Journal of Scientific Computing, 2019In this paper, we consider a non-convex problem which is the sum of \ell _0 -norm and a convex smooth function under a box constraint. We propose one proximal iterative hard thresholding type method with an extrapolation step for acceleration and establish its global convergence results. In detail, the sequence generated by the proposed method globally converges to a local minimizer of the objective function. Finally, we conduct numerical experiments to show the proposed method’s effectiveness on comparison with some other efficient methods.
@article{zhang2019new, title = {A New Proximal Iterative Hard Thresholding Method with Extrapolation for L0 Minimization}, author = {Zhang, Xue and Zhang, Xiaoqun}, journal = {Journal of Scientific Computing}, volume = {79}, number = {2}, pages = {809--826}, year = {2019}, publisher = {Springer US New York}, } - Journal
Noise Suppression in Image-Domain Multi-Material Decomposition for Dual-Energy CT
IEEE Transactions on Biomedical Engineering, 2019OBJECTIVE: Dual-energy CT (DECT) strengthens the material characterization and quantification due to its capability of material discrimination. The image-domain multi-material decomposition (MMD) via matrix inversion suffers from serious degradation of the signal-to-noise ratios (SNRs) of the decomposed images, and thus the clinical application of DECT is limited. In this paper, we propose a noise suppression algorithm based on the noise propagation for image-domain MMD. METHODS: The noise in the decomposed images only distributes in two perpendicular directions and is suppressed by estimating the center of mass of the same-material pixel group vertically along the principal axis where the noise disturbance is minimal. The proposed method is evaluated using the line-pair and contrast-rod slices of the Catphan©600 phantom and one patient data set. We compared the proposed method with the direct inversion and the block-matching and three-dimensional (BM3D) filtration methods. RESULTS: The results of Catphan©600 phantom and the patient show that the proposed method successfully suppresses the noise of the basis material images by one order of magnitude and preserves the spatial resolution of the decomposed images. Compared with the BM3D filtration method, the proposed method maintains the texture distribution of the decomposed images at the same SNR and the accuracy of the electron density measurement. CONCLUSION: The algorithm achieves effective noise suppression compared with the BM3D filtration while maintaining the spatial distribution of the decomposed material images. It is, thus, attractive for advanced clinical applications using DECT.
@article{jiang2019noise, title = {Noise Suppression in Image-Domain Multi-Material Decomposition for Dual-Energy CT}, author = {Jiang, Yangkang and Xue, Yi and Lyu, Qihui and Xu, Lei and Luo, Chen and Yang, Pengfei and Yang, Chunlin and Wang, Jing and Hu, Xi and Zhang, Xiaoqun and others}, journal = {IEEE Transactions on Biomedical Engineering}, volume = {67}, number = {2}, pages = {523--535}, year = {2019}, publisher = {IEEE}, }
2018
- Conference
Local Convergence Properties of SAGA/Prox-SVRG and Acceleration
In International Conference on Machine Learning (ICML), 2018In this paper, we present a local convergence anal- ysis for a class of stochastic optimisation meth- ods: the proximal variance reduced stochastic gradient methods, and mainly focus on SAGA (Defazio et al., 2014) and Prox-SVRG (Xiao & Zhang, 2014). Under the assumption that the non-smooth component of the optimisation prob- lem is partly smooth relative to a smooth mani- fold, we present a unified framework for the local convergence analysis of SAGA/Prox-SVRG: (i) the sequences generated by the methods are able to identify the smooth manifold in a finite num- ber of iterations; (ii) then the sequence enters a local linear convergence regime. Furthermore, we discuss various possibilities for accelerating these algorithms, including adapting to better lo- cal parameters, and applying higher-order deter- ministic/stochastic optimisation methods which can achieve super-linear convergence. Several concrete examples arising from machine learning are considered to demonstrate the obtained result.
@inproceedings{poon2018local, title = {Local Convergence Properties of SAGA/Prox-SVRG and Acceleration}, author = {Poon, Clarice and Liang, Jingwei and Sch{\"o}nlieb, Carola-Bibiane}, booktitle = {International Conference on Machine Learning (ICML)}, pages = {4124--4132}, year = {2018}, } - Journal
Local Linear Convergence Analysis of Primal–Dual Splitting Methods
Optimization, 2018In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal-Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal-Dual splitting can be specialized to cover existing ones on Forward-Backward splitting and Douglas-Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal-Dual splitting methods, but also the insights on how to accelerate them in practice.
@article{liang2018local, title = {Local Linear Convergence Analysis of Primal--Dual Splitting Methods}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, journal = {Optimization}, number = {6}, pages = {821--853}, year = {2018}, publisher = {Taylor \& Francis}, } - Journal
Image-Domain Multimaterial Decomposition for Dual-Energy CT Based on Prior Information of Material Images
Medical physics, 2018Dual‐Energy Computed Tomography (DECT) is of great interest in medical imaging, security inspection, and nondestructive testing. Most DECT reconstruction methods focus on producing two material images with different linear attenuation coefficients. However, the ability to reconstruct three or more basis materials is clinically and industrially important. Under the assumption that there are at most three materials in each pixel, there are a few methods that estimate multiple material images from DECT measurements by enforcing sum‐to‐one and a box constraint ([0 1]) derived from both the volume and mass conservation assumption. The recently proposed image‐domain multimaterial decomposition (MMD) method introduces edge‐preserving regularization for each material image. It enforces the assumption that there are at most three materials in each pixel using a time‐consuming loop over all possible material triplets. However, this method neglects relations among material images. We propose a new image‐domain MMD model for DECT that considers the prior information that different material images have common or complementary edges and encourages sparsity of material composition in each pixel using regularization. The proposed PWLS‐TNV‐ℓ 0 method uses penalized weighted least‐square (PWLS) reconstruction with three regularization terms. The first term is total nuclear variation (TNV) that accounts for the image property that basis material images share common or complementary boundaries and each material image is piecewise constant. The second term is an ℓ 0 norm that encourages each pixel containing a small subset of material types out of several possible materials. The third term is a characteristic function based on sum‐to‐one and a box constraint derived from the volume and mass conservation assumption. We apply the Alternating Direction Method of Multipliers (ADMM) to optimize the cost function of the PWLS‐TNV‐ℓ 0 method. We evaluated the proposed method on a simulated digital phantom, Catphan©600 phantom and patient’s pelvis data. We implemented two existing image‐domain MMD methods for DECT, the Direct Inversion and the PWLS‐EP‐LOOP method. We initialized the PWLS‐TNV‐ℓ 0 method and the PWLS‐EP‐LOOP method with the results of the Direct Inversion method and compared performance of the proposed method with that of the PWLS‐EP‐LOOP method. The proposed method lowers the bias of decomposed material fractions by 84.47% in the digital phantom study, by 99.50% in the Catphan©600 phantom study, and by 99.64% in the pelvis patient study, respectively, compared to the PWLS‐EP‐LOOP method. The proposed method reduces noise standard deviation (STD) by 52.21% in the Catphan©600 phantom study, and by 16.74% in the patient’s pelvis study, compared to the PWLS‐EP‐LOOP method. The proposed method increases volume fraction accuracy by 6.04%,20.55%, and 13.46% for the digital phantom, the Catphan©600 phantom, and the patient’s pelvis study, respectively, compared to the PWLS‐EP‐LOOP method. Compared with the PWLS‐EP‐LOOP method, the root mean square percentage error [RMSE(%)] of electron densities in the Catphan©600 phantom is decreased by about 7.39%. We proposed an image‐domain MMD method, PWLS‐TNV‐ℓ 0 , for DECT. The PWLS‐TNV‐ℓ 0 method takes low rank property of material image gradients, sparsity of material composition and mass and volume conservation into consideration. The proposed method suppresses noise, reduces cross contamination, and improves accuracy in the decomposed material images, compared to the PWLS‐EP‐LOOP method.
@article{ding2018image, title = {Image-Domain Multimaterial Decomposition for Dual-Energy CT Based on Prior Information of Material Images}, author = {Ding, Qiaoqiao and Niu, Tianye and Zhang, Xiaoqun and Long, Yong}, journal = {Medical physics}, volume = {45}, number = {8}, pages = {3614--3626}, year = {2018}, publisher = {Wiley Online Library}, } - Journal
PET-MRI Joint Reconstruction by Joint Sparsity Based Tight Frame Regularization
SIAM Journal on Imaging Sciences, 2018Recent technical advances lead to the coupling of PET and MRI scanners, enabling one to acquire functional and anatomical data simultaneously. In this paper, we propose a tight frame based PET-MRI joint reconstruction model via the joint sparsity of tight frame coefficients. In addition, a nonconvex balanced approach is adopted to take the different regularities of PET and MRI images into account. To solve the nonconvex and nonsmooth model, a proximal alternating minimization algorithm is proposed, and the global convergence is present based on the Kurdyka–Łojasiewicz property. Finally, the numerical experiments show that our proposed models achieve better performance over the existing PET-MRI joint reconstruction models.
@article{choi2018pet, title = {PET-MRI Joint Reconstruction by Joint Sparsity Based Tight Frame Regularization}, author = {Choi, Jae Kyu and Bao, Chenglong and Zhang, Xiaoqun}, journal = {SIAM Journal on Imaging Sciences}, volume = {11}, number = {2}, pages = {1179--1204}, year = {2018}, publisher = {Society for Industrial and Applied Mathematics}, } - Preprint
Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CT
arXiv preprint arXiv:1801.09533, 2018Statistical image reconstruction (SIR) methods for X-ray CT produce high-quality and accurate images, while greatly reducing patient exposure to radiation. When further reducing X-ray dose to an ultra-low level by lowering the tube current, photon starvation happens and electronic noise starts to dominate, which introduces negative or zero values into the raw measurements. These non-positive values pose challenges to post-log SIR methods that require taking the logarithm of the raw data, and causes artifacts in the reconstructed images if simple correction methods are used to process these non-positive raw measurements. The raw data at ultra-low dose deviates significantly from Poisson or shifted Poisson statistics for pre-log data and from Gaussian statistics for post-log data. This paper proposes a novel SIR method called MPG (mixed Poisson-Gaussian). MPG models the raw noisy measurements using a mixed Poisson-Gaussian distribution that accounts for both the quantum noise and electronic noise. MPG is able to directly use the negative and zero values in raw data without any pre-processing. MPG cost function contains a reweighted least square data-fit term, an edge preserving regularization term and a non-negativity constraint term. We use Alternating Direction Method of Multipliers (ADMM) to separate the MPG optimization problem into several sub-problems that are easier to solve. Our results on 3D simulated cone-beam data set and synthetic helical data set generated from clinical data indicate that the proposed MPG method reduces noise and decreases bias in the reconstructed images, comparing with the conventional filtered back projection (FBP), penalized weighted least-square (PWLS) and shift Poisson (SP) method for ultra-low dose CT (ULDCT) imaging.
@article{ding2018statistical, title = {Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-Ray CT}, author = {Ding, Qiaoqiao and Long, Yong and Zhang, Xiaoqun and Fessler, Jeffrey A}, journal = {arXiv preprint arXiv:1801.09533}, year = {2018}, } - Journal
PET-MRI Joint Reconstruction with Common Edge Weighted Total Variation Regularization
Inverse Problems, 2018Driven by recent developments of PET-MRI scanners, simultaneous reconstruction of dual-modality has gained considerable research interest. The purpose of this paper is to propose a joint reconstruction model by utilizing complementary information of dual-modality to improve reconstruction quality of individual images. We propose a total variation based joint regularization with an adaptively estimated common edge indicator function as a weight. The common edge function takes into account the shared structures of two modalities in a flexible way. A proximal alternating algorithm is adopted to recover dual-modality images and the common edge, and the convergence of the overall numerical scheme is established. Finally, numerical tests for PET and MRI under different noise levels and subsampling patterns show that the proposed approach obtains favorable results compared to some existing methods.
@article{zhang2018pet, title = {PET-MRI Joint Reconstruction with Common Edge Weighted Total Variation Regularization}, author = {Zhang, Ying and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {34}, number = {6}, pages = {065006}, year = {2018}, publisher = {IOP Publishing}, } - Conference
Image Reconstruction by Splitting Deep Learning Regularization from Iterative Inversion
In Medical Image Computing and Computer Assisted Intervention (MICCAI), 2018Image reconstruction from downsampled and corrupted measurements, such as fast MRI and low dose CT, is mathematically ill-posed inverse problem. In this work, we propose a general and easy-to-use reconstruction method based on deep learning techniques. In order to address the intractable inversion of general inverse problems, we propose to train a network to refine intermediate images from classical reconstruction procedure to the ground truth, i.e. the intermediate images that satisfy the data consistence will be fed into some chosen denoising networks or generative networks for denoising and removing artifact in each iterative stage. The proposed approach involves only techniques of conventional image reconstruction and usual image representation/denoising deep network learning, without a specifically designed and complicated network structures for a certain physical forward operator. Extensive experiments on MRI reconstruction applied with both stack auto-encoder networks and generative adversarial nets demonstrate the efficiency and accuracy of the proposed method compared with other image reconstruction algorithms.
@inproceedings{liu2018image, title = {Image Reconstruction by Splitting Deep Learning Regularization from Iterative Inversion}, author = {Liu, Jiulong and Kuang, Tao and Zhang, Xiaoqun}, booktitle = {Medical Image Computing and Computer Assisted Intervention (MICCAI)}, pages = {224--231}, year = {2018}, organization = {Springer International Publishing}, }
2017
- Journal
Activity Identification and Local Linear Convergence of Forward–Backward-Type Methods
SIAM Journal on Optimization, 2017In this paper, we consider a class of Forward–Backward (FB) splitting methods that includes several variants (e.g., inertial schemes, FISTA) for minimizing the sum of two proper convex and lower semicontinuous functions, one of which has a Lipschitz continuous gradient, and the other is partly smooth relative to a smooth active manifold M. We propose a unified framework, under which we show that this class of FB-type algorithms (i) correctly identifies the active manifold in a finite number of iterations (finite activity identification), and (ii) then enters a local linear convergence regime, which we characterize precisely in terms of the structure of the underlying active manifold. We also establish and explain why FISTA (with convergent sequences) locally oscillates and can be locally slower than FB. These results may have numerous applications including in signal/image processing, sparse recovery and machine learning. Indeed, the obtained results explain the typical behaviour that has been observed numerically for many problems in these fields such as the Lasso, the group Lasso, the fused Lasso and the nuclear norm minimization to name only a few.
@article{liang2017activity, title = {Activity Identification and Local Linear Convergence of Forward--Backward-Type Methods}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, journal = {SIAM Journal on Optimization}, volume = {27}, number = {1}, pages = {408--437}, year = {2017}, publisher = {SIAM}, } - Journal
Local Convergence Properties of Douglas–Rachford and Alternating Direction Method of Multipliers
Journal of Optimization Theory and Applications, 2017The Douglas-Rachford and alternating direction method of multipliers are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of Douglas-Rachford (resp. alternating direction method of multipliers) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when the two functions (resp. their conjugates) are partly smooth relative to their respective smooth submanifolds, we show that Douglas-Rachford (resp. alternating direction method of multipliers) (i) identifies these manifolds in finite time; (ii) enters a local linear convergence regime. When both functions are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified submanifolds. Under polyhedrality of both functions, we also provide conditions sufficient for finite convergence. The obtained results are illustrated by several concrete examples and supported by numerical experiments.
@article{liang2017local, title = {Local Convergence Properties of Douglas--Rachford and Alternating Direction Method of Multipliers}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, journal = {Journal of Optimization Theory and Applications}, volume = {172}, number = {3}, pages = {874--913}, year = {2017}, publisher = {Plenum Press}, } - Journal
CUSTOM: A Calibration Region Recovery Approach for Highly Subsampled Dynamic Parallel Magnetic Resonance Imaging
Journal of Mathematical Imaging and Vision, 2017We propose a recovery approach for highly subsampled dynamic parallel MRI image without auto-calibration signals (ACSs) or prior knowledge of coil sensitivity maps. By exploiting the between-frame redundancy of dynamic parallel MRI data, we first introduce a new low-rank matrix recovery-based model, termed as calibration using spatial–temporal matrix (CUSTOM), for ACSs recovery. The recovered ACSs from data are used for estimating coil sensitivity maps and further dynamic image reconstruction. The proposed non-convex and non-smooth minimization for the CUSTOM step is solved by a proximal alternating linearized minimization method, and we provide its convergence result for this specific minimization problem. Numerical experiments on several highly subsampled test data demonstrate that the proposed overall approach outperforms other state-of-the-art methods for calibrationless dynamic parallel MRI reconstruction.
@article{zhang2017custom, title = {CUSTOM: A Calibration Region Recovery Approach for Highly Subsampled Dynamic Parallel Magnetic Resonance Imaging}, author = {Zhang, Xue and Hou, Likun and Gao, Hao and Zhang, Xiaoqun}, journal = {Journal of Mathematical Imaging and Vision}, volume = {57}, pages = {366--380}, year = {2017}, publisher = {Springer US}, } - Journal
Dynamic SPECT Reconstruction with Temporal Edge Correlation
Inverse Problems, 2017In dynamic imaging, a key challenge is to reconstruct image sequences with high temporal resolution from strong undersampling projections due to a relatively slow data acquisition speed. In this paper, we propose a variational model using the infimal convolution of Bregman distance with respect to total variation to model edge dependence of sequential frames. The proposed model is solved via an alternating iterative scheme, for which each subproblem is convex and can be solved by existing algorithms. The proposed model is formulated under both Gaussian and Poisson noise assumption and the simulation on two sets of dynamic images shows the advantage of the proposed method compared to previous methods.
@article{ding2017dynamic, title = {Dynamic SPECT Reconstruction with Temporal Edge Correlation}, author = {Ding, Qiaoqiao and Burger, Martin and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {34}, number = {1}, pages = {014005}, year = {2017}, publisher = {IOP Publishing}, } - Conference
Image-Domain Multi-Material Decomposition for Dual-Energy CT via Total Nuclear Norm and \ell_0 Norm
In Proceedings of the 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully3D), 2017@inproceedings{ding2018totalnuclear, title = {Image-Domain Multi-Material Decomposition for Dual-Energy CT via Total Nuclear Norm and $\ell_0$ Norm}, author = {Ding, Qiaoqiao and Niu, Tianye and Zhang, Xiaoqun and Long, Yong}, booktitle = {Proceedings of the 14th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully3D)}, pages = {154--159}, year = {2017}, }
2016
- Thesis
Convergence Rates of First-Order Operator Splitting Methods
Normandie Université; GREYC CNRS UMR 6072, 2016This manuscript is concerned with convergence analysis of first-order operator splitting methods that are ubiquitous in modern non-smooth optimization. It consists of three main theoretical advances on this class of methods, namely global convergence rates, novel operator splitting schemes and local linear convergence. First, we propose global (sub-linear) and local (linear) convergence rates for the inexact Krasnosel’skii-Mann iteration built from non-expansive operators, and its application to a variety of monotone operator splitting schemes. Then we design two novel multi-step inertial operator splitting algorithms, both in the convex and non-convex settings, and prove their global convergence. Finally, building on the key concept of partial smoothness, we present a unified and sharp local linear convergence analysis for the class of first-order proximal splitting methods for optimization. We show that for all these algorithms, under appropriate non-degeneracy conditions, the iterates generated by each of these methods will (i) identify the involved partial smooth manifolds in finite time, and then (ii) enter a local linear convergence regime. The linear convergence rates are characterized precisely based on the structure of the optimization problems, that of the proximal splitting scheme, and the geometry of the identified active manifolds. Our theoretical findings are systematically illustrated on applications arising from inverse problems, signal/image processing and machine learning.
@phdthesis{liang2016convergence, title = {Convergence Rates of First-Order Operator Splitting Methods}, author = {Liang, Jingwei}, year = {2016}, school = {Normandie Universit{\'e}; GREYC CNRS UMR 6072}, } - Journal
Convergence Rates with Inexact Non-Expansive Operators
Mathematical Programming, 2016In this paper, we present a convergence rate analysis for the inexact Krasnosel’skiĭ-Mann iteration built from non-expansive operators. The presented results include two main parts: we first establish the global pointwise and ergodic iteration-complexity bounds; then, under a metric sub-regularity assumption, we establish a local linear convergence for the distance of the iterates to the set of fixed points. The obtained results can be applied to analyze the convergence rate of various monotone operator splitting methods in the literature, including the Forward-Backward splitting, the Generalized Forward-Backward, the Douglas-Rachford splitting, alternating direction method of multipliers and Primal-Dual splitting methods. For these methods, we also develop easily verifiable termination criteria for finding an approximate solution, which can be seen as a generalization of the termination criterion for the classical gradient descent method. We finally develop a parallel analysis for the non-stationary Krasnosel’skiĭ-Mann iteration.
@article{liang2016inexact, title = {Convergence Rates with Inexact Non-Expansive Operators}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, journal = {Mathematical Programming}, volume = {159}, number = {1}, pages = {403--434}, year = {2016}, publisher = {Springer Berlin Heidelberg}, } - Conference
A Multi-Step Inertial Forward-Backward Splitting Method for Non-Convex Optimization
In Advances in Neural Information Processing Systems (NeurIPS), 2016In this paper, we propose a multi-step inertial Forward–Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a Lipschitz continuous gradient. We first prove global convergence of the scheme with the help of the Kurdyka-Łojasiewicz property. Then, when the non-smooth part is also partly smooth relative to a smooth submanifold, we establish finite identification of the latter and provide sharp local linear convergence analysis. The proposed method is illustrated on a few problems arising from statistics and machine learning.
@inproceedings{liang2016multi, title = {A Multi-Step Inertial Forward-Backward Splitting Method for Non-Convex Optimization}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, pages = {4035--4043}, year = {2016}, } - Journal
Fast Sparse Reconstruction: Greedy Inverse Scale Space Flows
Math. Comp., 2016In this paper we analyze the connection between the recently proposed adaptive inverse scale space methods for basis pursuit and the well-known orthogonal matching pursuit method for the recovery of sparse solutions to underdetermined linear systems. Furthermore, we propose a new greedy sparse recovery method, which approximates ℓ 1 \ell ^1 minimization more closely. A variant of our new approach can increase the support of the current iterate by many indices at once, resulting in an extremely efficient algorithm. Our new method has the advantage that there is a simple criterion to determine a posteriori if an ℓ 1 \ell ^1 minimizer was found. Numerical comparisons with orthogonal matching pursuit, weak orthogonal matching pursuit, hard thresholding pursuit and compressive sampling matching pursuit underline that our methods indeed inherit some advantageous properties from the inverse scale space flow.
@article{moller2016fast, title = {Fast Sparse Reconstruction: Greedy Inverse Scale Space Flows}, author = {Moller, Michael and Zhang, Xiaoqun}, journal = {Math. Comp.}, volume = {85}, pages = {179--208}, year = {2016}, } - Journal
Pansharpening Image Fusion Using Cross-Channel Correlation: A Framelet-Based Approach
Journal of Mathematical Imaging and Vision, 2016This paper aims at developing a variational model for pansharpening image fusion. To resolve the ill-posedness of image fusion, we propose a new regularization technique that explores the cross-channel correlation of different spectral channels in wavelet tight frame (or framelet) domain. Besides using a regular cross-channel sparsity prior (Inverse Probl Imaging 7(3):777–794, 2013 ), the proposed model also makes efficient use of the panchromatic image as a guidance for image feature alignment. An ADMM-based iterative scheme is derived for solving the proposed model, and its performance is tested on several datasets including natural images, aerial images, and real multispectral satellite images. Numerical results suggest that the proposed approach works well on the testing datasets and outperforms some state-of-the-art algorithms in comparison.
@article{hou2016pansharpening, title = {Pansharpening Image Fusion Using Cross-Channel Correlation: A Framelet-Based Approach}, author = {Hou, Likun and Zhang, Xiaoqun}, journal = {Journal of Mathematical Imaging and Vision}, volume = {55}, pages = {36--49}, year = {2016}, publisher = {Springer US}, } - Journal
Multi-Scale Features Extraction from Baseline Structure MRI for MCI Patient Classification and AD Early Diagnosis
Neurocomputing, 2016@article{hu2016multi, title = {Multi-Scale Features Extraction from Baseline Structure MRI for MCI Patient Classification and AD Early Diagnosis}, author = {Hu, Kun and Wang, Yijue and Chen, Kewei and Hou, Likun and Zhang, Xiaoqun}, journal = {Neurocomputing}, volume = {175}, pages = {132--145}, year = {2016}, publisher = {Elsevier}, } - Journal
A Primal-Dual Fixed Point Algorithm for Multi-Block Convex Minimization
Journal of Computational Mathematics, 2016We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block problems and illustrate how practical and fully decoupled schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier (ADMM) are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.
@article{chen2016primal, title = {A Primal-Dual Fixed Point Algorithm for Multi-Block Convex Minimization}, author = {Chen, Peijun and Huang, Jianguo and Zhang, Xiaoqun}, journal = {Journal of Computational Mathematics}, pages = {723--738}, year = {2016}, publisher = {Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy}, } - Journal
Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation
Journal of Computational Mathematics, 2016X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered backprojection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the horizontally truncated projections. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.
@article{choi2016limited, title = {Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation}, author = {Choi, Jae Kyu and Dong, Bin and Zhang, Xiaoqun}, journal = {Journal of Computational Mathematics}, volume = {34}, number = {6}, pages = {575--589}, publisher = {Global Science Press}, year = {2016}, } - Journal
A Two-Stage Low Rank Approach for Calibrationless Dynamic Parallel Magnetic Resonance Image Reconstruction
Journal of Scientific Computing, 2016Parallel magnetic resonance imaging (MRI) is an imaging technique by acquiring a reduced amount of data in Fourier domain with multiple receiver coils. To recover the underlying imaging object, one often needs the explicit knowledge of coil sensitivity maps, or some additional fully acquired data blocks called the auto-calibration signals (ACS). In this paper, we show that by exploiting the between-frame redundancy of dynamic parallel MRI data, it is possible to achieve simultaneous coil sensitivity map estimation and image sequence reconstruction. Specially, we introduce a novel two-stage approach for dynamic parallel MRI reconstruction without pre-calibrating the coil sensitivity maps nor additionally acquiring any fully sampled ACS. Numerical experiments demonstrate that, the performance of the proposed approach is better than other state-of-the-art approaches for calibrationless dynamic parallel MRI reconstruction.
@article{hou2016two, title = {A Two-Stage Low Rank Approach for Calibrationless Dynamic Parallel Magnetic Resonance Image Reconstruction}, author = {Hou, Likun and Gao, Hao and Zhang, Xiaoqun}, journal = {Journal of Scientific Computing}, volume = {69}, pages = {1014--1032}, year = {2016}, publisher = {Springer US}, } - Journal
Simultaneous Reconstruction and Segmentation for Dynamic SPECT Imaging
Inverse Problems, 2016This work deals with the reconstruction of dynamic images that incorporate characteristic dynamics in certain subregions, as arising for the kinetics of many tracers in emission tomography (SPECT, PET). We make use of a basis function approach for the unknown tracer concentration by assuming that the region of interest can be divided into subregions with spatially constant concentration curves. Applying a regularised variational framework reminiscent of the Chan-Vese model for image segmentation we simultaneously reconstruct both the labelling functions of the subregions as well as the subconcentrations within each region. Our particular focus is on applications in SPECT with the Poisson noise model, resulting in a Kullback–Leibler data fidelity in the variational approach. We present a detailed analysis of the proposed variational model and prove existence of minimisers as well as error estimates. The latter apply to a more general class of problems and generalise existing results in literature since we deal with a nonlinear forward operator and a nonquadratic data fidelity. A computational algorithm based on alternating minimisation and splitting techniques is developed for the solution of the problem and tested on appropriately designed synthetic data sets. For those we compare the results to those of standard EM reconstructions and investigate the effects of Poisson noise in the data.
@article{burger2016simultaneous, title = {Simultaneous Reconstruction and Segmentation for Dynamic SPECT Imaging}, author = {Burger, Martin and Rossmanith, Carolin and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {32}, number = {10}, pages = {104002}, year = {2016}, publisher = {IOP Publishing}, } - Journal
A Wavelet Frame Method with Shape Prior for Ultrasound Video Segmentation
SIAM Journal on Imaging Sciences, 2016Ultrasound video segmentation is a challenging task due to low contrast, shadow effects, complex noise statistics, and the need for high precision and efficiency in real time applications such as operation navigation and therapy planning. In this paper, we propose a wavelet frame based video segmentation framework incorporating different noise statistics and sequential distance shape priors. The proposed individual frame nonconvex segmentation model is solved by a proximal alternating minimization algorithm, and the convergence of the scheme is established based on the recently proposed Kurdyka–Łojasiewicz property. The performance of the overall method is demonstrated through numerical results on two real ultrasound video data sets. The proposed method is shown to achieve better results compared to the related level sets models and edge indicator shape priors, in terms of both segmentation quality and computational time.
@article{liu2016wavelet, title = {A Wavelet Frame Method with Shape Prior for Ultrasound Video Segmentation}, author = {Liu, Jiulong and Zhang, Xiaoqun and Dong, Bin and Shen, Zuowei and Gu, Lixu}, journal = {SIAM Journal on Imaging Sciences}, volume = {9}, number = {2}, pages = {495--519}, year = {2016}, publisher = {Society for Industrial and Applied Mathematics}, } - Conference
Modeling Mixed Poisson-Gaussian Noise in Statistical Image Reconstruction for X-Ray CT
In Proceedings of the 4th International Conference on Image Formation in X-Ray Computed Tomography, 2016@inproceedings{ding2016modeling, title = {Modeling Mixed Poisson-Gaussian Noise in Statistical Image Reconstruction for X-Ray CT}, author = {Ding, Qiaoqiao and Long, Yong and Zhang, Xiaoqun and Fessler, Jeffrey A}, booktitle = {Proceedings of the 4th International Conference on Image Formation in X-Ray Computed Tomography}, pages = {399--402}, year = {2016}, } - Journal
TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT
IEEE transactions on medical imaging, 2016This work develops a material reconstruction method for spectral CT, namely Total Image Constrained Material Reconstruction (TICMR), to maximize the utility of projection data in terms of both spectral information and high signal-to-noise ratio (SNR). This is motivated by the following fact: when viewed as a spectrally-integrated measurement, the projection data can be used to reconstruct a total image without spectral information, which however has a relatively high SNR; when viewed as a spectrally-resolved measurement, the projection data can be utilized to reconstruct the material composition, which however has a relatively low SNR. The material reconstruction synergizes material decomposition and image reconstruction, i.e., the direct reconstruction of material compositions instead of a two-step procedure that first reconstructs images and then decomposes images. For material reconstruction with high SNR, we propose TICMR with nonlocal total variation (NLTV) regularization. That is, first we reconstruct a total image using spectrally-integrated measurement without spectral binning, and build the NLTV weights from this image that characterize nonlocal image features; then the NLTV weights are incorporated into a NLTV-based iterative material reconstruction scheme using spectrally-binned projection data, so that these weights serve as a high-SNR reference to regularize material reconstruction. Note that the nonlocal property of NLTV is essential for material reconstruction, since material compositions may have significant local intensity variations although their structural information is often similar. In terms of solution algorithm, TICMR is formulated as an iterative reconstruction method with the NLTV regularization, in which the nonlocal divergence is utilized based on the adjoint relationship. The alternating direction method of multipliers is developed to solve this sparsity optimization problem. The proposed TICMR method was validated using both simulated and experimental data. In comparison with FBP and total-variation-based iterative method, TICMR had improved image quality, e.g., contrast-to-noise ratio and spatial resolution.
@article{liu2016ticmr, title = {TICMR: Total Image Constrained Material Reconstruction via Nonlocal Total Variation Regularization for Spectral CT}, author = {Liu, Jiulong and Ding, Huanjun and Molloi, Sabee and Zhang, Xiaoqun and Gao, Hao}, journal = {IEEE transactions on medical imaging}, volume = {35}, number = {12}, pages = {2578--2586}, year = {2016}, publisher = {IEEE}, } - Journal
Image Restoration by Minimizing Zero Norm of Wavelet Frame Coefficients
Inverse problems, 2016In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ 0 -norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka–Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ 0 -norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.
@article{bao2016image, title = {Image Restoration by Minimizing Zero Norm of Wavelet Frame Coefficients}, author = {Bao, Chenglong and Dong, Bin and Hou, Likun and Shen, Zuowei and Zhang, Xiaoqun and Zhang, Xue}, journal = {Inverse problems}, volume = {32}, number = {11}, pages = {115004}, year = {2016}, publisher = {IOP Publishing}, } - Journal
Operator Splitting Methods in Compressive Sensing and Sparse Approximation
Splitting Methods in Communication, Imaging, Science, and Engineering, 2016Compressive sensing and sparse approximation have many emerging applications, and are a relatively new driving force for the development of splitting methods in optimization. Many sparse coding problems are well described by variational models with ℓ 1 -norm penalties and constraints that are designed to promote sparsity. Successful algorithms need to take advantage of the separable structure of potentially complicated objectives by “splitting” them into simpler pieces and iteratively solving a sequence of simpler convex minimization problems. In particular, isolating ℓ 1 terms from the rest of the objective leads to simple soft thresholding updates or ℓ 1 ball projections. A few basic splitting techniques can be used to design a huge variety of relevant algorithms. This chapter will focus on operator splitting strategies that are based on proximal operators, duality, and alternating direction methods. These will be explained in the context of basis pursuit variants and through compressive sensing applications.
@article{goldstein2016operator, title = {Operator Splitting Methods in Compressive Sensing and Sparse Approximation}, author = {Goldstein, Tom and Zhang, Xiaoqun}, journal = {Splitting Methods in Communication, Imaging, Science, and Engineering}, pages = {301--343}, year = {2016}, publisher = {Springer International Publishing}, } - Journal
A Primal-Dual Fixed Point Algorithm for Minimization of the Sum of Three Convex Separable Functions
Fixed Point Theory and Applications, 2016Many problems arising in image processing and signal recovery with multi-regularization and constraints can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. In this paper, we propose a primal-dual fixed point (PDFP) scheme to solve the above class of problems. The proposed algorithm for three-block problems is a symmetric and fully splitting scheme, only involving an explicit gradient, a linear transform, and the proximity operators which may have a closed-form solution. We study the convergence of the proposed algorithm and illustrate its efficiency through examples on fused LASSO and image restoration with non-negative constraint and sparse regularization.
@article{chen2016three, title = {A Primal-Dual Fixed Point Algorithm for Minimization of the Sum of Three Convex Separable Functions}, author = {Chen, Peijun and Huang, Jianguo and Zhang, Xiaoqun}, journal = {Fixed Point Theory and Applications}, volume = {2016}, pages = {1--18}, year = {2016}, publisher = {Springer International Publishing}, } - Journal
A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography
SIAM Journal on Imaging Sciences, 2016The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar method produces reconstructions with sharper edges and improved contrast. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain, thereby increasing the radius of the low-pass filter. The algorithm is tested on numerically simulated noisy EIT data and demonstrates significant improvements in edge preservation and contrast which can be highly valuable for absolute EIT imaging.
@article{hamilton2016hybrid, title = {A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography}, author = {Hamilton, Sarah J and Reyes, Juan Manuel and Siltanen, Samuli and Zhang, Xiaoqun}, journal = {SIAM Journal on Imaging Sciences}, volume = {9}, number = {2}, pages = {770--793}, year = {2016}, publisher = {Society for Industrial and Applied Mathematics}, }
2015
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Activity Identification and Local Linear Convergence of Douglas–Rachford/ADMM under Partial Smoothness
In International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2015Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within this class of algorithms, Douglas-Rachford (DR) and ADMM are designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of DR (resp. ADMM) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when both of the two functions (resp. their conjugates) are partly smooth relative to their respective manifolds, we show that DR (resp. ADMM) identifies these manifolds in finite time. Moreover, when these manifolds are affine or linear, we prove that DR/ADMM is locally linearly convergent with a rate in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified manifolds. This is illustrated by several concrete examples and supported by numerical experiments.
@inproceedings{liang2015activity, title = {Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel and Luke, Russell}, booktitle = {International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)}, pages = {642--653}, year = {2015}, organization = {Springer, Cham}, } - Journal
Retinex by Higher Order Total Variation L1 Decomposition
Journal of Mathematical Imaging and Vision, 2015In this paper, we propose a reflectance and illumination decomposition model for the Retinex problem via high-order total variation and L^1 decomposition. Based on the observation that illumination varies smoother than reflectance, we propose a convex variational model which can effectively decompose the gradient field of images into salient edges and relatively smoother illumination field through the first- and second-order total variation regularizations. The proposed model can be efficiently solved by a primal-dual splitting method. Numerical experiments on both grayscale and color images show the strength of the proposed model with applications to Retinex illusions, medical image bias field removal, and color image shadow correction.
@article{liang2015retinex, title = {Retinex by Higher Order Total Variation L1 Decomposition}, author = {Liang, Jingwei and Zhang, Xiaoqun}, journal = {Journal of Mathematical Imaging and Vision}, volume = {52}, number = {3}, pages = {345--355}, year = {2015}, publisher = {Springer}, } - Journal
Dynamic SPECT Reconstruction from Few Projections: A Sparsity Enforced Matrix Factorization Approach
Inverse Problems, 2015The reconstruction of dynamic images from few projection data is a challenging problem, especially when noise is present and when the dynamic images are vary fast. In this paper, we propose a variational model, sparsity enforced matrix factorization (SEMF), based on low rank matrix factorization of unknown images and enforced sparsity constraints for representing both coefficients and bases. The proposed model is solved via an alternating iterative scheme for which each subproblem is convex and involves the efficient alternating direction method of multipliers (ADMM). The convergence of the overall alternating scheme for the nonconvex problem relies upon the Kurdyka–Łojasiewicz property, recently studied by Attouch et al (2010 Math. Oper. Res. 35 438 ) and Attouch et al (2013 Math. Program. 137 91 ). Finally our proof-of-concept simulation on 2D dynamic images shows the advantage of the proposed method compared to conventional methods.
@article{ding2015dynamic, title = {Dynamic SPECT Reconstruction from Few Projections: A Sparsity Enforced Matrix Factorization Approach}, author = {Ding, Qiaoqiao and Zan, Yunlong and Huang, Qiu and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {31}, number = {2}, pages = {025004}, year = {2015}, publisher = {IOP Publishing}, } - Journal
Interpolation and Denoising of High-Dimensional Seismic Data by Learning a Tight Frame
Geophysics, 2015Sparse transforms play an important role in seismic signal processing steps, such as prestack noise attenuation and data reconstruction. Analytic sparse transforms (so-called implicit dictionaries), such as the Fourier, Radon, and curvelet transforms, are often used to represent seismic data. There are situations, however, in which the complexity of the data requires adaptive sparse transform methods, whose basis functions are determined via learning methods. We studied an application of the data-driven tight frame (DDTF) method to noise suppression and interpolation of high-dimensional seismic data. Rather than choosing a model beforehand (for example, a family of lines, parabolas, or curvelets) to fit the data, the DDTF derives the model from the data itself in an optimum manner. The process of estimating the basis function from the data can be summarized as follows: First, the input data are divided into small blocks to form training sets. Then, the DDTF algorithm is applied on the training sets to estimate the dictionary. The DDTF is typically embodied as an explicit dictionary, and a sparsity-promoting algorithm is used to obtain an optimized tight frame representation of the observed data. The computational time and redundancy is controlled by the block overlap of the training set. Finally, the learned dictionary is used to represent the observed data and to estimate data at unobserved spatial positions. Our numerical results showed that the proposed methodology is capable of recovering n-dimensional prestack seismic data under different signal-to-noise ratio scenarios. We determined that subtle features tend to be better preserved with the DDTF method in comparison with standard Fourier and directional transform reconstruction methods.
@article{yu2015interpolation, title = {Interpolation and Denoising of High-Dimensional Seismic Data by Learning a Tight Frame}, author = {Yu, Siwei and Ma, Jianwei and Zhang, Xiaoqun and Sacchi, Mauricio D}, journal = {Geophysics}, volume = {80}, number = {5}, pages = {V119--V132}, year = {2015}, publisher = {Society of Exploration Geophysicists}, } - Journal
A Reweighted L2 Method for Image Restoration with Poisson and Mixed Poisson-Gaussian Noise
Inverse Problems and Imaging, 2015We study weighted l^2 fidelity in variational models for Poisson noise related image restoration problems. Gaussian approximation to Poisson noise statistic is adopted to deduce weighted l^2 fidelity. Different from the traditional weighted l^2 approximation, we propose a reweighted l^2 fidelity with sparse regularization by wavelet frame. Based on the split Bregman algorithm introduced in [21], the proposed numerical scheme is composed of three easy subproblems that involve quadratic minimization, soft shrinkage and matrix vector multiplications. Unlike usual least square approximation of Poisson noise, we dynamically update the underlying noise variance from previous estimate. The solution of the proposed algorithm is shown to be the same as the one obtained by minimizing Kullback-Leibler divergence fidelity with the same regularization. This reweighted l^2 formulation can be easily extended to mixed Poisson-Gaussian noise case. Finally, the efficiency and quality of the proposed algorithm compared to other Poisson noise removal methods are demonstrated through denoising and deblurring examples. Moreover, mixed Poisson-Gaussian noise tests are performed on both simulated and real digital images for further illustration of the performance of the proposed method.
@article{li2015reweighted, title = {A Reweighted L2 Method for Image Restoration with Poisson and Mixed Poisson-Gaussian Noise}, author = {Li, Jia and Shen, Zuowei and Yin, Rujie and Zhang, Xiaoqun}, journal = {Inverse Problems and Imaging}, volume = {9}, number = {3}, pages = {875--894}, year = {2015}, } - Journal
A Note on the Complexity of Proximal Iterative Hard Thresholding Algorithm
Journal of the Operations Research Society of China, 2015The iterative hard thresholding (IHT) algorithm is a powerful and efficient algorithm for solving \ell _0 -regularized problems and inspired many applications in sparse-approximation and image-processing fields. Recently, some convergence results are established for the proximal scheme of IHT, namely proximal iterative hard thresholding (PIHT) algorithm (Blumensath and Davies, in J Fourier Anal Appl 14:629–654, 2008 ; Hu et al., Methods 67:294–303, 2015 ; Lu, Math Program 147:125–154, 2014 ; Trzasko et al., IEEE/SP 14th Workshop on Statistical Signal Processing, 2007 ) on solving the related \ell _0 -optimization problems. However, the complexity analysis for the PIHT algorithm is not well explored. In this paper, we aim to provide some complexity estimations for the PIHT sequences. In particular, we show that the complexity of the sequential iterate error is at o (1 / k ). Under the assumption that the objective function is composed of a quadratic convex function and \ell _0 regularization, we show that the PIHT algorithm has \mathbb R -linear convergence rate. Finally, we illustrate some applications of this algorithm for compressive sensing reconstruction and sparse learning and validate the estimated error bounds.
@article{zhang2015note, title = {A Note on the Complexity of Proximal Iterative Hard Thresholding Algorithm}, author = {Zhang, Xue and Zhang, Xiao-Qun}, journal = {Journal of the Operations Research Society of China}, volume = {3}, number = {4}, pages = {459--473}, year = {2015}, publisher = {Operations Research Society of China Beijing}, } - Journal
5D Respiratory Motion Model Based Image Reconstruction Algorithm for 4D Cone-Beam Computed Tomography
Inverse Problems, 20154D cone-beam computed tomography (4DCBCT) reconstructs a temporal sequence of CBCT images for the purpose of motion management or 4D treatment in radiotherapy. However the image reconstruction often involves the binning of projection data to each temporal phase, and therefore suffers from deteriorated image quality due to inaccurate or uneven binning in phase, e.g., under the non-periodic breathing. A 5D model has been developed as an accurate model of (periodic and non-periodic) respiratory motion. That is, given the measurements of breathing amplitude and its time derivative, the 5D model parametrizes the respiratory motion by three time-independent variables, i.e., one reference image and two vector fields. In this work we aim to develop a new 4DCBCT reconstruction method based on 5D model. Instead of reconstructing a temporal sequence of images after the projection binning, the new method reconstructs time-independent reference image and vector fields with no requirement of binning. The image reconstruction is formulated as a optimization problem with total-variation regularization on both reference image and vector fields, and the problem is solved by the proximal alternating minimization algorithm, during which the split Bregman method is used to reconstruct the reference image, and the Chambolle’s duality-based algorithm is used to reconstruct the vector fields. The convergence analysis of the proposed algorithm is provided for this nonconvex problem. Validated by the simulation studies, the new method has significantly improved image reconstruction accuracy due to no binning and reduced number of unknowns via the use of the 5D model.
@article{liu20155d, title = {5D Respiratory Motion Model Based Image Reconstruction Algorithm for 4D Cone-Beam Computed Tomography}, author = {Liu, Jiulong and Zhang, Xue and Zhang, Xiaoqun and Zhao, Hongkai and Gao, Yu and Thomas, David and Low, Daniel A and Gao, Hao}, journal = {Inverse Problems}, volume = {31}, number = {11}, pages = {115007}, year = {2015}, publisher = {IOP Publishing}, }
2014
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Local Linear Convergence of Forward–Backward under Partial Smoothness
In Advances in Neural Information Processing Systems (NeurIPS), 2014In this paper, we consider the Forward–Backward proximal splitting algorithm to minimize the sum of two proper closed convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relatively to an active manifold M. We propose a generic framework in which we show that the Forward–Backward (i) correctly identifies the active manifold M in a finite number of iterations, and then (ii) enters a local linear convergence regime that we characterize precisely. This gives a grounded and unified explanation to the typical behaviour that has been observed numerically for many problems encompassed in our framework, including the Lasso, the group Lasso, the fused Lasso and the nuclear norm regularization to name a few. These results may have numerous applications including in signal/image processing processing, sparse recovery and machine learning.
@inproceedings{liang2014local, title = {Local Linear Convergence of Forward--Backward under Partial Smoothness}, author = {Liang, Jingwei and Fadili, Jalal and Peyr{\'e}, Gabriel}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, volume = {27}, pages = {1970--1978}, year = {2014}, } - Journal
Seismic Data Restoration via Data-Driven Tight Frame
Geophysics, 2014Restoration/interpolation of missing traces plays a crucial role in the seismic data processing pipeline. Efficient restoration methods have been proposed based on sparse signal representation in a transform domain such as Fourier, wavelet, curvelet, and shearlet transforms. Most existing methods are based on transforms with a fixed basis. We considered an adaptive sparse transform for restoration of data with complex structures. In particular, we evaluated a data-driven tight-frame-based sparse regularization method for seismic data restoration. The main idea of the data-driven tight frame (TF) is to adaptively learn a set of framelet filters from the currently interpolated data, under which the data can be more sparsely represented; hence, the sparsity-promoting l1-norm (SPL1) minimization methods can produce better restoration results by using the learned filters. A split inexact Uzawa algorithm, which can be viewed as a generalization of the alternating direction of multiplier method (ADMM), was applied to solve the presented SPL1 model. Numerical tests were performed on synthetic and real seismic data for restoration of randomly missing traces over a regular data grid. Our experiments showed that our proposed method obtains the state-of-the-art restoration results in comparison with the traditional Fourier-based projection onto convex sets, the tight-frame-based method, and the recent shearlet regularization ADMM method.
@article{liang2014seismic, title = {Seismic Data Restoration via Data-Driven Tight Frame}, author = {Liang, Jingwei and Ma, Jianwei and Zhang, Xiaoqun}, journal = {Geophysics}, volume = {79}, number = {3}, pages = {65--74}, year = {2014}, publisher = {Society of Exploration Geophysicists}, } - Journal
Domain Decomposition Methods for Nonlocal Total Variation Image Restoration
Journal of Scientific Computing, 2014Nonlocal total variation (TV) regularization (Gilboa and Osher in Multiscale Model Simulat 7(3): 1005–1028, 2008 ; Zhou and Schölkopf in Pattern recognition, proceedings of the 27th DAGM symposium. Springer, Berlin, pp 361–368, 2005 ) has been widely used for the natural image processing, since it is able to preserve repetitive textures and details of images. However, its applications have been limited in practice, due to the high computational cost for large scale problems. In this paper, we apply domain decomposition methods (DDMs) (Xu et al. in Inverse Probl Imag 4(3):523–545, 2010 ) to the nonlocal TV image restoration. By DDMs, the original problem is decomposed into much smaller subproblems defined on subdomains. Each subproblem can be efficiently solved by the split Bregman algorithm and Bregmanized operator splitting algorithm in Zhang et al. (SIAM J Imaging Sci 3(3):253–276, 2010 ). Furthermore, by using coloring technique on the domain decomposition, all subproblems defined on subdomains with same colors can be computed in parallel. Our numerical examples demonstrate that the proposed methods can efficiently solve the nonlocal TV based image restoration problems, such as denoising, deblurring and inpainting. It can be computed in parallel with a considerable speedup ratio and speedup efficiency.
@article{chang2014domain, title = {Domain Decomposition Methods for Nonlocal Total Variation Image Restoration}, author = {Chang, Huibin and Zhang, Xiaoqun and Tai, Xue-Cheng and Yang, Danping}, journal = {Journal of Scientific Computing}, volume = {60}, pages = {79--100}, year = {2014}, publisher = {Springer US}, } - Journal
Nonlocal Patch-Based Image Inpainting Through Minimization of a Sparsity Promoting Nonconvex Functional
Dept. Math., Univ. California Irvine, Irvine, CA, USA, Tech. Rep, 2014@article{esser2014nonlocal, title = {Nonlocal Patch-Based Image Inpainting Through Minimization of a Sparsity Promoting Nonconvex Functional}, author = {Esser, ERNIE and Zhang, XIAOQUN}, journal = {Dept. Math., Univ. California Irvine, Irvine, CA, USA, Tech. Rep}, volume = {3}, pages = {13}, year = {2014}, } - Journal
Forward–Backward Splitting Method for Quantitative Photoacoustic Tomography
Inverse problems, 2014Quantitative photoacoustic tomography (PAT) reconstructs optical maps using ultrasonic measurements, with improved resolution from conventional optical imaging due to significantly smaller acoustic scattering than optical scattering for detecting signals in depth. In this work, formulating quantitative PAT as a nonlinear least-squares problem with l 1 -norm sparsity regularization, we develop an efficient gradient-based reconstruction algorithm using a forward–backward splitting method, and prove its convergence for such a nonconvex problem.
@article{zhang2014forward, title = {Forward--Backward Splitting Method for Quantitative Photoacoustic Tomography}, author = {Zhang, Xue and Zhou, Weifeng and Zhang, Xiaoqun and Gao, Hao}, journal = {Inverse problems}, volume = {30}, number = {12}, pages = {125012}, year = {2014}, publisher = {IOP Publishing}, }
2013
- Journal
Wavelet Frame Based Color Image Demosaicing
Inverse Problems and Imaging, 2013Color image demosaicing consists in recovering full resolution color information from color-filter-array (CFA) samples with 66.7% amount of missing data. Most of the existing color demosaicing methods [14, 25, 16, 2, 26] are based on interpolation from inter-channel correlation and local geometry, which are not robust to highly saturated color images with small geometric features. In this paper, we introduce wavelet frame based methods by using a sparse wavelet [8, 22, 9, 23] approximation of individual color channels and color differences that recovers both geometric features and color information. The proposed models can be efficiently solved by Bregmanized operator splitting algorithm [27]. Numerical simulations of two datasets: McM and Kodak PhotoCD, show that our method outperforms other existing methods in terms of PSNR and visual quality.
@article{liang2013wavelet, title = {Wavelet Frame Based Color Image Demosaicing}, author = {Liang, Jingwei and Li, Jia and Shen, Zuowei and Zhang, Xiaoqun}, journal = {Inverse Problems and Imaging}, volume = {7}, number = {3}, pages = {777--794}, year = {2013}, } - Journal
A Primal–Dual Fixed Point Algorithm for Convex Separable Minimization with Applications to Image Restoration
Inverse Problems, 2013Recently, the minimization of a sum of two convex functions has received considerable interest in a variational image restoration model. In this paper, we propose a general algorithmic framework for solving a separable convex minimization problem from the point of view of fixed point algorithms based on proximity operators (Moreau 1962 C. R. Acad. Sci., Paris I 255 2897–99). Motivated by proximal forward–backward splitting proposed in Combettes and Wajs (2005 Multiscale Model. Simul. 4 1168–200) and fixed point algorithms based on the proximity operator (FP 2 O) for image denoising (Micchelli et al 2011 Inverse Problems 27 45009–38), we design a primal–dual fixed point algorithm based on the proximity operator (PDFP 2 O κ for κ ∈ [0, 1)) and obtain a scheme with a closed-form solution for each iteration. Using the firmly nonexpansive properties of the proximity operator and with the help of a special norm over a product space, we achieve the convergence of the proposed PDFP 2 O κ algorithm. Moreover, under some stronger assumptions, we can prove the global linear convergence of the proposed algorithm. We also give the connection of the proposed algorithm with other existing first-order methods. Finally, we illustrate the efficiency of PDFP 2 O κ through some numerical examples on image supper-resolution, computerized tomographic reconstruction and parallel magnetic resonance imaging. Generally speaking, our method PDFP 2 O (κ = 0) is comparable with other state-of-the-art methods in numerical performance, while it has some advantages on parameter selection in real applications.
@article{chen2013primal, title = {A Primal--Dual Fixed Point Algorithm for Convex Separable Minimization with Applications to Image Restoration}, author = {Chen, Peijun and Huang, Jianguo and Zhang, Xiaoqun}, journal = {Inverse Problems}, volume = {29}, number = {2}, pages = {33}, year = {2013}, } - Journal
Wavelet Frame Based Multiphase Image Segmentation
SIAM Journal on Imaging Sciences, 2013Wavelet frames have been successfully applied to various image restoration problems, such as denoising, inpainting, and deblurring. However, they are rarely used in geometric applications, except for the recent work of [B. Dong, A. Chien, and Z. Shen, Commun. Math. Sci., 9 (2011), pp. 551–559; B. Dong and Z. Shen, in Proceedings of the SPIE, Vol. 8401, 2012, 840102]. Motivated by the theoretical connection between wavelet frame based and total variation based image restoration models recently established in [J.-F. Cai, B. Dong, S. Osher, and Z. Shen, J. Amer. Math. Soc., 25 (2012), pp. 1033–1089], we propose here a convex multiphase segmentation model based on wavelet frame transform. The proposed model allows us to automatically identify complex tubular structures, including blood vessels, leaf vein systems, etc. Numerical results show that our method can extract more details than existing variational methods especially when the image contains different scales of structures. The proposed method is parallelized, and its efficiency is further improved by a graphics processing unit implementation. In addition, we analyze the connection between solutions of the convexified model and the original binary constrained model.
@article{tai2013wavelet, title = {Wavelet Frame Based Multiphase Image Segmentation}, author = {Tai, Cheng and Zhang, Xiaoqun and Shen, Zuowei}, journal = {SIAM Journal on Imaging Sciences}, volume = {6}, number = {4}, pages = {2521--2546}, year = {2013}, publisher = {SIAM}, } - Journal
A Primal-Dual Fixed Point Algorithm Based on Proximity Operator for Convex Set Constrained Separable Problem
J. Nanjing Norm. Univ. Nat. Sci. Ed, 2013@article{chen2013constrained, title = {A Primal-Dual Fixed Point Algorithm Based on Proximity Operator for Convex Set Constrained Separable Problem}, author = {Chen, Peijun and Huang, Jianguo and Zhang, Xiaoqun}, journal = {J. Nanjing Norm. Univ. Nat. Sci. Ed}, volume = {36}, number = {3}, pages = {1--5}, year = {2013}, }
2012
- Journal
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing, 2012In this paper, we consider 3D Bioluminescence tomography (BLT) source reconstruction from Poisson data in three dimensional space. With a priori information of sources sparsity and MAP estimation of Poisson distribution, we study the minimization of Kullback-Leihbler divergence with ℓ 1 and ℓ 0 regularization. We show numerically that although several ℓ 1 minimization algorithms are efficient for compressive sensing, they fail for BLT reconstruction due to the high coherence of the measurement matrix columns and high nonlinearity of Poisson fitting term. Instead, we propose a novel greedy algorithm for ℓ 0 regularization to reconstruct sparse solutions for BLT problem. Numerical experiments on synthetic data obtained by the finite element methods and Monte-Carlo methods show the accuracy and efficiency of the proposed method.
@article{zhang2012novel, title = {A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography}, author = {Zhang, Xiaoqun and Lu, Yujie and Chan, Tony}, journal = {Journal of Scientific Computing}, pages = {1--17}, year = {2012}, publisher = {Springer}, }
2011
- Journal
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing, 2011百篇最具影响国际学术论文全部产生自2011年引用次数高于学科均线的论文，从SCI收录的我国第一作者论文中选取，论文学术影响的主要文献计量指标为论 文创新性（是否获得重大基金和项目支持）、发表论文的期刊水平（期刊的主要指标所在学科位置）、是否处于研究前沿和是否属于研究热点（即年被引次数）、合著论文中我国作者的主导性（以我为主的国际合作情况）、论文的文献类型（只计Article和Review类型）、论文的参考文献情况（与该学科国际平均水平的比较）和论文的国际知名度（是否发表于世界著名期刊）。这些遴选指标的选取是为了保证了论文的领先型和相对优势。
In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration (Osher et al., Multiscale Model. Simul. 4(2):460–489, 2005) based methods, such as linearized Bregman (Osher et al., Commun. Math. Sci. 8(1):93–111, 2010; Cai et al., SIAM J. Imag. Sci. 2(1):226–252, 2009, CAM Report 09-28, UCLA, March 2009; Yin, CAAM Report, Rice University, 2009) and split Bregman (Goldstein and Osher, SIAM J. Imag. Sci., 2, 2009). The convergence of the general algorithm framework is proved under mild assumptions. The applications to ℓ 1 basis pursuit, TV−L 2 minimization and matrix completion are demonstrated. Finally, the numerical examples show the algorithms proposed are easy to implement, efficient, stable and flexible enough to cover a wide variety of applications.
@article{zhang2011unified, title = {A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration}, author = {Zhang, Xiaoqun and Burger, Martin and Osher, Stanley}, journal = {Journal of Scientific Computing}, volume = {46}, pages = {20--46}, year = {2011}, publisher = {Springer US}, }
2010
- Journal
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences, 2010Bregman methods introduced in [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460–489] to image processing are demonstrated to be an efficient optimization method for solving sparse reconstruction with convex functionals, such as the \ell^1 norm and total variation [W. Yin, S. Osher, D. Goldfarb, and J. Darbon, SIAM J. Imaging Sci., 1 (2008), pp. 143–168; T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323–343]. In particular, the efficiency of this method relies on the performance of inner solvers for the resulting subproblems. In this paper, we propose a general algorithm framework for inverse problem regularization with a single forward-backward operator splitting step [P. L. Combettes and V. R. Wajs, Multiscale Model. Simul., 4 (2005), pp. 1168–1200], which is used to solve the subproblems of the Bregman iteration. We prove that the proposed algorithm, namely, Bregmanized operator splitting (BOS), converges without fully solving the subproblems. Furthermore, we apply the BOS algorithm and a preconditioned one for solving inverse problems with nonlocal functionals. Our numerical results on deconvolution and compressive sensing illustrate the performance of nonlocal total variation regularization under the proposed algorithm framework, compared to other regularization techniques such as the standard total variation method and the wavelet-based regularization method.
@article{zhang2010bregmanized, title = {Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction}, author = {Zhang, Xiaoqun and Burger, Martin and Bresson, Xavier and Osher, Stanley}, journal = {SIAM Journal on Imaging Sciences}, volume = {3}, number = {3}, pages = {253--276}, year = {2010}, } - Journal
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
SIAM Journal on Imaging Sciences, 2010We generalize the primal-dual hybrid gradient (PDHG) algorithm proposed by Zhu and Chan in [An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration, CAM Report 08-34, UCLA, Los Angeles, CA, 2008] to a broader class of convex optimization problems. In addition, we survey several closely related methods and explain the connections to PDHG. We point out convergence results for a modified version of PDHG that has a similarly good empirical convergence rate for total variation (TV) minimization problems. We also prove a convergence result for PDHG applied to TV denoising with some restrictions on the PDHG step size parameters. We show how to interpret this special case as a projected averaged gradient method applied to the dual functional. We discuss the range of parameters for which these methods can be shown to converge. We also present some numerical comparisons of these algorithms applied to TV denoising, TV deblurring, and constrained l_1 minimization problems.
@article{esser2010general, title = {A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science}, author = {Esser, Ernie and Zhang, Xiaoqun and Chan, Tony}, journal = {SIAM Journal on Imaging Sciences}, volume = {3}, number = {4}, pages = {1015--1046}, year = {2010}, } - Journal
Image Recovery via Nonlocal Operators
Journal of Scientific Computing, 2010This paper considers two nonlocal regularizations for image recovery, which exploit the spatial interactions in images. We get superior results using preprocessed data as input for the weighted functionals. Applications discussed include image deconvolution and tomographic reconstruction. The numerical results show our method outperforms some previous ones.
@article{lou2010image, title = {Image Recovery via Nonlocal Operators}, author = {Lou, Yifei and Zhang, Xiaoqun and Osher, Stanley and Bertozzi, Andrea}, journal = {Journal of Scientific Computing}, volume = {42}, number = {2}, pages = {185--197}, year = {2010}, publisher = {Springer US}, } - Journal
Wavelet Inpainting by Nonlocal Total Variation
Inverse problems and Imaging, 2010Wavelet inpainting problem consists of filling in missed data in the wavelet domain. In [17], Chan, Shen, and Zhou proposed an efficient method to recover piecewise constant or smooth images by combining total variation regularization and wavelet representations. In this paper, we extend it to nonlocal total variation regularization in order to recover textures and local geometry structures simultaneously. Moreover, we apply an efficient algorithm framework for both local and nonlocal regularizers. Extensiveexperimental results on a variety of loss scenarios and naturalimages validate the performance of this approach.
@article{zhang2010wavelet, title = {Wavelet Inpainting by Nonlocal Total Variation}, author = {Zhang, Xiaoqun and Chan, Tony F}, journal = {Inverse problems and Imaging}, volume = {4}, number = {1}, pages = {191--210}, year = {2010}, publisher = {American Institute of Mathematical Sciences}, }
2009
- Journal
Source Reconstruction for Spectrally-Resolved Bioluminescence Tomography with Sparse a Priori Information
Optics express, 2009Through restoration of the light source information in small animals in vivo, optical molecular imaging, such as fluorescence molecular tomography (FMT) and bioluminescence tomography (BLT), can depict biological and physiological changes observed using molecular probes. A priori information plays an indispensable role in tomographic reconstruction. As a type of a priori information, the sparsity characteristic of the light source has not been sufficiently considered to date. In this paper, we introduce a compressed sensing method to develop a new tomographic algorithm for spectrally-resolved bioluminescence tomography. This method uses the nature of the source sparsity to improve the reconstruction quality with a regularization implementation. Based on verification of the inverse crime, the proposed algorithm is validated with Monte Carlo-based synthetic data and the popular Tikhonov regularization method. Testing with different noise levels and single/multiple source settings at different depths demonstrates the improved performance of this algorithm. Experimental reconstruction with a mouse-shaped phantom further shows the potential of the proposed algorithm.
@article{lu2009source, title = {Source Reconstruction for Spectrally-Resolved Bioluminescence Tomography with Sparse a Priori Information}, author = {Lu, Yujie and Zhang, Xiaoqun and Douraghy, Ali and Stout, David and Tian, Jie and Chan, Tony F and Chatziioannou, Arion F}, journal = {Optics express}, volume = {17}, number = {10}, pages = {8062--8080}, year = {2009}, publisher = {Optica Publishing Group}, }
2005
- Conference
Total Variation Based Fourier Reconstruction and Regularization for Computer Tomography
In IEEE Nuclear Science Symposium Conference Record (NSS), 2005The paper develops a tomographic reconstruction and regularization method based on a total variation minimization constrained by the knowledge of the input intervals the Fourier coefficients belong to. Experiments show that the approach outperforms classical reconstruction methods such as direct Fourier method (DFM), filtered back-projection (FBP) and Tikhonov iterative method (TIM), both in terms of PSNR (an objective mean-square error) and visual quality, especially in the case of noisy or sparse data. In addition the resulting algorithm requires a number of operations of O(N/sup 2/ log N) only, and is therefore faster than ordinary iterative methods, such as space-based TIM.
@inproceedings{zhang2005total, title = {Total Variation Based Fourier Reconstruction and Regularization for Computer Tomography}, author = {Zhang, Xiao-Qun and Froment, Jacques}, booktitle = {IEEE Nuclear Science Symposium Conference Record (NSS)}, volume = {4}, pages = {2332--2336}, year = {2005}, organization = {IEEE}, } - Conference
Constrained Total Variation Minimization and Application in Computerized Tomography
In International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), 2005We present a simple framework for solving different ill-posed inverse problems in image processing by means of constrained total variation minimizations. We argue that drawbacks commonly attributed to total variation algorithms (slowness and incomplete fit to the image model) can be easily bypassed by performing only a few number of iterations in our optimization process. We illustrate this approach in the context of computerized tomography, that comes down to inverse a Radon transform obtained by illuminating an object by straight and parallel beams of x-rays. This problem is ill-posed because only a finite number of line integrals can be measured, resulting in an incomplete coverage of the frequency plane and requiring, for a direct Fourier reconstruction, frequencies interpolation from a polar to a Cartesian grid. We introduce a new method of interpolation based on a total variation minimization constrained by the knowledge of frequency coefficients in the polar grid, subject to a Lipschitz regularity assumption. The experiments show that our algorithm is able to avoid Gibbs and noise oscillations associated to the direct Fourier method, and that it outperforms classical reconstruction methods such as filtered backprojection and Rudin-Osher-Fatemi total variation restoration, in terms of both PSNR and visual quality.
@inproceedings{zhang2005constrained, title = {Constrained Total Variation Minimization and Application in Computerized Tomography}, author = {Zhang, Xiao-Qun and Froment, Jacques}, booktitle = {International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)}, pages = {456--472}, year = {2005}, organization = {Springer Berlin Heidelberg Berlin, Heidelberg}, }
2004
- Journal
The Regularity of Random Graph Directed Self-Similar Sets
Acta Mathematica Scientia, 2004@article{zhang2004regularity, title = {The Regularity of Random Graph Directed Self-Similar Sets}, author = {Zhang, Xiaoqun and Liu, Yanyan}, journal = {Acta Mathematica Scientia}, volume = {24}, number = {3}, pages = {485--492}, year = {2004}, publisher = {No longer published by Elsevier}, }
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