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Theory and fast learned solver for ℓ¹-TV regularization

INVERSE PROBLEMS 2025年第1期41卷

作者： Liu, Xinling Wang, Jianjun Jin, Bangti Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China China West Normal Univ China West Normal Univ Sichuan Prov Sch Math & Informat Key Lab Optimizat Theory & Applicat Nanchong 637009 Peoples R China Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China

The & ell;(1) and total variation (TV) penalties have been used successfully in many areas, and the combination of the & ell;(1) and TV penalties can lead to further improved performance. In this work, we investigate the mathematical theory and numerical algorithms for the & ell;(1)-TV model in the context of signal recovery: we derive the sample complexity of the & ell;(1)-TV model for recovering signals with sparsity and gradient sparsity. Also we propose a novel algorithm (PGM-ISTA) for the regularized & ell;(1)-TV problem, and establish its global convergence and parameter selection criteria. Furthermore, we construct a fast learned solver (LPGM-ISTA) by unrolling PGM-ISTA. The results for the experiment on ECG signals show the superior performance of LPGM-ISTA in terms of recovery accuracy and computational efficiency.

关键词： & ell (1)-TV regularization sample complexity learned solver algorithm unrolling

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A model-based deep learning approach to interpretable impact force localization and reconstruction

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 224卷

作者： Zhou, Rui Qiao, Baijie Jiang, Liangliang Cheng, Wei Yang, Xiuyue Wang, Yanan Chen, Xuefeng Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Natl Key Lab Aerosp Power Syst & Plasma Technol Xian 710049 Peoples R China Beijing Inst Astronaut Syst Engn Beijing 10076 Peoples R China

Model-based and deep learning-based methods have been widely studied for force identification. However, model-based methods usually have high computational complexity and face challenges in parameter setting, while the generic network structures in deep learning methods are mostly designed empirically. In this paper, a model-based deep learning network is proposed to simultaneously localize and reconstruct impact f[orces. The proposed network, dubbed NSC-Net, is obtained by unrolling the iterative shrinkage-thresholding algorithm (ISTA) for the non- negative sparse coding (NSC) model. NSC-Net combines the interpretability of the model-based ISTA with the powerful parameter learning capability of deep learning. The transfer matrix is embedded into the network as physical information through learnable scaling. The structure of NSC-Net is based on explicit theoretical analysis, which enhances its interpretability in terms of structural design. In contrast to ISTA, the parameters in NSC-Net can be trained end-to-end from the training data without manual setting. Simulations and experiments on composite panels are conducted to validate the performance of the proposed method. The results demonstrate that NSC-Net accurately localizes and reconstructs impact forces, outperforming both ISTA and learned iterative shrinkage-thresholding algorithm (LISTA) network. Additionally, NSC-Net exhibits excellent noise immunity. Furthermore, the systematic approach of constructing an algorithm unrolling network for impact force identification is summarized, aiming to facilitate further related research.

关键词： Impact force identification algorithm unrolling Interpretable deep learning Composite structures Structural health monitoring

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Sparse Bayesian Learning Unfolding Network for Efficient DoA Estimation in Low SNR

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IEEE Transactions on Vehicular Technology 2025年

作者： Lv, Liujie Wu, Sheng Su, Yi Jiang, Chunxiao Kuang, Linling Beijing University of Posts and Telecommunications School of Information and Communication Engineering Beijing100876 China Beijing Institute of Remote Sensing Equipment China Tsinghua University Tsinghua Space Center the Beijing National Research Center for Information Science and Technology Beijing100084 China

Compressive sensing (CS) algorithms have demonstrated superior direction-of-arrival (DoA) estimation accuracy in the low signal-to-noise ratio (SNR) regime by exploiting inherent angular sparsity. However, traditional CS-based algorithms require numerous iterations to gradually converge well, resulting in high computational complexity and limiting their applicability in practical systems. In this paper, we propose a sparse Bayesian learning (SBL) unfolding network for superior and efficient DoA estimation. Specifically, the SBL framework is unfolded into a series of cascaded SBL layers, each corresponding to a hyperparameter update. Within each SBL layer, we introduce a Convolution-Transformer based source power estimation network (CTsNet) to better capture angular sparsity and generate more efficient update rule for the signal hyperparameter. Simultaneously, a convolution-based noise variance estimation network (CnNet) is proposed for accurate noise variance estimation, which controls the sharpness of the peak spectrum and affects the iterations of the signal hyperparameter. Simulation results demonstrate that the proposed method not only performs better than existing methods in terms of estimation accuracy and angular resolution, but also exhibits lower computational complexity compared with other SBL-based algorithms. © 2025 IEEE.

关键词： algorithm unrolling compressive sensing Direction of arrival (DoA) estimation model-driven deep learning sparse Bayesian learning

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A Bayesian Based Deep unrolling algorithm for Single-Photon Lidar Systems

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2022年第4期16卷 762-774页

作者： Koo, Jakeoung Halimi, Abderrahim McLaughlin, Stephen Heriot Watt Univ Sch Engn & Phys Sci Edinburgh EH14 4AS Midlothian Scotland

Deploying 3D single-photon Lidar imaging in real world applications presents multiple challenges including imaging in high noise environments. Several algorithms have been proposed to address these issues based on statistical or learning-based frameworks. Statistical methods provide rich information about the inferred parameters but are limited by the assumed model correlation structures, while deep learning methods show state-of-the-art performance but limited inference guarantees, preventing their extended use in critical applications. This paper unrolls a statistical Bayesian algorithm into a new deep learning architecture for robust image reconstruction from single-photon Lidar data, i.e. the algorithm's iterative steps are converted into neural network layers. The resulting algorithm benefits from the advantages of both statistical and learning based frameworks, providing best estimates with improved network interpretability. Compared to existing learning-based solutions, the proposed architecture requires a reduced number of trainable parameters, is more robust to noise and mismodelling of the system impulse response function, and provides richer information about the estimates including uncertainty measures. Results on synthetic and real data show competitive results regarding the quality of the inference and computational complexity when compared to state-of-the-art algorithms.

关键词： Laser radar Photonics Deep learning Signal processing algorithms Three-dimensional displays Bayes methods Histograms 3D reconstruction Lidar single-photon imaging algorithm unrolling attention Bayesian inference

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GSISTA-Net: generalized structure ISTA networks for image compressed sensing based on optimized unrolling algorithm

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第34期83卷 80373-80387页

作者： Zeng, Chunyan Yu, Yan Wang, Zhifeng Xia, Shiyan Cui, Hao Wan, Xiangkui Hubei Univ Technol Hubei Key Lab High Efficiency Utilizat Solar Energ Nanli Rd Wuhan 430068 Peoples R China Cent China Normal Univ Dept Digital Media Technol Luoyu Rd Wuhan 430079 Peoples R China

Image compressed sensing technology, particularly algorithm unrolling networks, has garnered significant attention in the field of compressed sensing due to their interpretability and high performance. However, similar to traditional compressed sensing methods, algorithm unrolling networks update and transmit pixel-level image data through specific instances of algorithms, often failing to fully exploit the rich information encoded in image features. This limitation results in information loss and incomplete feature fusion. In this paper, we introduce a novel approach: the Generalized Structure Iterative Shrinkage Threshold algorithm (GSISTA), and present an algorithm extension network built upon GSISTA, referred to as GSISTA-Net. GSISTA-Net facilitates the efficient transfer of image feature information during the deep reconstruction stage through a jump connection structure. Additionally, it incorporates a dual-scale denoising module within the deep reconstruction stage to enhance denoising effectiveness. Our experimental results demonstrate that the proposed method surpasses the performance of five prominent state-of-the-art algorithms, specifically ReconNet, CSNet, ISTA-Net+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>+$$\end{document}, AMPNet, and OPINE-Net+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>+$$\end{document}, when evaluated in terms of both Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM).

关键词： algorithm unrolling Compressed sensing Image reconstruction Deep learning

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Deep, Convergent, Unrolled Half-Quadratic Splitting for Image Deconvolution

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2024年 10卷 574-588页

作者： Zhao, Yanan Li, Yuelong Zhang, Haichuan Monga, Vishal Eldar, Yonina C. Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Amazon Lab 126 San Jose CA 94089 USA Penn State Univ Dept Elect Engn State Coll PA 16801 USA Weizmann Inst Sci Fac Math & Comp Sci Dept Elect Engn IL-7610001 Rehovot Israel

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer-specific parameters are learned from training data. We propose an unrolling technique that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on image deblurring and unrolling the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parametrization scheme which enforces layer-specific parameters to asymptotically approach certain fixed points. Through extensive experimental studies, we verify that our approach achieves competitive performance with state-of-the-art unrolled layer-specific learning and significantly improves over the traditional HQS algorithm. We further establish convergence of the proposed unrolled network as the number of layers approaches infinity, and characterize its convergence rate. Our experimental verification involves simulations that validate the analytical results as well as comparison with state-of-the-art non-blind deblurring techniques on benchmark datasets. The merits of the proposed convergent unrolled network are established over competing alternatives, especially in the regime of limited training.

关键词： algorithm unrolling convergent deep neural networks image deblurring

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Robust PCA unrolling Network for Super-Resolution Vessel Extraction in X-Ray Coronary Angiography

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2022年第11期41卷 3087-3098页

作者： Qin, Binjie Mao, Haohao Liu, Yiming Zhao, Jun Lv, Yisong Zhu, Yueqi Ding, Song Chen, Xu Shanghai Jiao Tong Univ Sch Biomed Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Sch Continuing Educ Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Shanghai Jiao Tong Univ Affiliated Peoples Hosp 6 Dept Radiol Shanghai 200233 Peoples R China Shanghai Jiao Tong Univ Ren Ji Hosp Sch Med Dept Cardiol Shanghai 200127 Peoples R China Univ Calif Riverside Ctr Adv Neuroimaging Riverside CA 92521 USA

Although robust PCA has been increasingly adopted to extract vessels from X-ray coronary angiography (XCA) images, challenging problems such as inefficient vessel-sparsity modelling, noisy and dynamic background artefacts, and high computational cost still remain unsolved. Therefore, we propose a novel robust PCA unrolling network with sparse feature selection for super-resolution XCA vessel imaging. Being embedded within a patch-wise spatiotemporal super-resolution framework that is built upon a pooling layer and a convolutional long short-term memory network, the proposed network can not only gradually prune complex vessel-like artefacts and noisy backgrounds in XCA during network training but also iteratively learn and select the high-level spatiotemporal semantic information of moving contrast agents flowing in the XCA-imaged vessels. The experimental results show that the proposed method significantly outperforms state-of-the-art methods, especially in the imaging of the vessel network and its distal vessels, by restoring the intensity and geometry profiles of heterogeneous vessels against complex and dynamic backgrounds. The source code is available at https://***/Binjie-Qin/RPCA-UNet

关键词： Feature extraction Spatiotemporal phenomena Noise measurement Computational modeling Image segmentation Data mining Angiography algorithm unrolling RPCA unrolling network X-ray coronary angiography vessel extraction sparse feature selection super-resolution

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Learning to Optimize: A Primer and A Benchmark

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-59页

作者： Chen, Tianlong Chen, Xiaohan Chen, Wuyang Wang, Zhangyang Heaton, Howard Liu, Jialin Yin, Wotao Engn Univ Texas Austin Dept Elect & Comp Austin TX 78712 USA Typal LLC Typal Res Los Angeles CA 90064 USA Damo Acad Decis Intelligence Lab Alibaba US Bellevue WA 98004 USA

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engi-neering. It automates the design of an optimization method based on its performance on a set of training problems. This data-driven procedure generates methods that can efficiently solve problems similar to those in training. In sharp contrast, the typical and traditional designs of optimization methods are theory-driven, so they obtain performance guarantees over the classes of problems specified by the theory. The difference makes L2O suitable for repeatedly solving a particular optimization problem over a specific distribution of data, while it typically fails on out-of-distribution problems. The practicality of L2O depends on the type of target optimization, the chosen architecture of the method to learn, and the training procedure. This new paradigm has motivated a community of researchers to explore L2O and report their *** article is poised to be the first comprehensive survey and benchmark of L2O for continuous optimization. We set up taxonomies, categorize existing works and research directions, present insights, and identify open challenges. We benchmarked many existing L2O approaches on a few representative optimization problems. For reproducible research and fair benchmarking purposes, we released our software implementation and data in the package Open-L2O at https://***/VITA-Group/Open-L2O.

关键词： learning to optimize meta learning optimization algorithm unrolling

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Attention-Guided Low-Rank Tensor Completion

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2024年第12期46卷 9818-9833页

作者： Truong Thanh Nhat Mai Lam, Edmund Y. Lee, Chul Dongguk Univ Dept Multimedia Engn Seoul 04620 South Korea Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China

Low-rank tensor completion (LRTC) aims to recover missing data of high-dimensional structures from a limited set of observed entries. Despite recent significant successes, the original structures of data tensors are still not effectively preserved in LRTC algorithms, yielding less accurate restoration results. Moreover, LRTC algorithms often incur high computational costs, which hinder their applicability. In this work, we propose an attention-guided low-rank tensor completion (AGTC) algorithm, which can faithfully restore the original structures of data tensors using deep unfolding attention-guided tensor factorization. First, we formulate the LRTC task as a robust factorization problem based on low-rank and sparse error assumptions. Low-rank tensor recovery is guided by an attention mechanism to better preserve the structures of the original data. We also develop implicit regularizers to compensate for modeling inaccuracies. Then, we solve the optimization problem by employing an iterative technique. Finally, we design a multistage deep network by unfolding the iterative algorithm, where each stage corresponds to an iteration of the algorithm;at each stage, the optimization variables and regularizers are updated by closed-form solutions and learned deep networks, respectively. Experimental results for high dynamic range imaging and hyperspectral image restoration show that the proposed algorithm outperforms state-of-the-art algorithms.

关键词： Low-rank tensor completion robust tensor factorization algorithm unrolling high dynamic range (HDR) imaging hyperspectral image (HSI) restoration

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Robust Stochastically-Descending Unrolled Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 5484-5499页

作者： Hadou, Samar Naderializadeh, Navid Ribeiro, Alejandro Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA Duke Univ Dept Biostat & Bioinformat Durham NC 27705 USA

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled networks are still open theoretical problems. To tackle these problems, we provide deep unrolled architectures with a stochastic descent nature by imposing descending constraints during training. The descending constraints are forced layer by layer to ensure that each unrolled layer takes, on average, a descent step toward the optimum during training. We theoretically prove that the sequence constructed by the outputs of the unrolled layers is then guaranteed to converge for in-distribution problems. We then analyze the generalizability to certain out-of-distribution (OOD) shifts in the optimization problems being solved. Our analysis shows that the descending nature imposed by the proposed constraints is transferable under these distribution shifts, subject to a generalization error, thereby providing the unrolled networks with OOD robustness. We numerically assess unrolled architectures trained with the proposed constraints in two different applications, including the sparse coding using learnable iterative shrinkage and thresholding algorithm (LISTA) and image inpainting using proximal generative flow (GLOW-Prox), and demonstrate the performance and robustness advantages of the proposed method.

关键词： Convergence Standards Trajectory Training Perturbation methods Optimization Signal processing algorithms Iterative algorithms Robustness Artificial neural networks algorithm unrolling deep unfolding learning to optimize constrained learning

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