SIAM J. Imaging Sci.最新文献_第4页

WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for Inverse Problems with Approximate Sharpness Conditions 近似锐度条件下逆问题的线性收敛一阶原对偶算法

SIAM J. Imaging Sci. Pub Date : 2022-09-01 DOI: 10.1137/21m1455000

Matthew J. Colbrook

{"title":"WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for Inverse Problems with Approximate Sharpness Conditions","authors":"Matthew J. Colbrook","doi":"10.1137/21m1455000","DOIUrl":"https://doi.org/10.1137/21m1455000","url":null,"abstract":"Sharpness conditions directly control the recovery performance of restart schemes for first-order optimization methods without the need for restrictive assumptions such as strong convexity. However, they are challenging to apply in the presence of noise or approximate model classes (e.g., approximate sparsity). We provide a first-order method: weighted, accelerated, and restarted primal-dual (WARPd), based on primal-dual iterations and a novel restart-reweight scheme. Under a generic approximate sharpness condition, WARPd achieves stable linear convergence to the desired vector. Many problems of interest fit into this framework. For example, we analyze sparse recovery in compressed sensing, low-rank matrix recovery, matrix completion, TV regularization, minimization of ∥Bx∥l1 under constraints (l-analysis problems for general B), and mixed regularization problems. We show how several quantities controlling recovery performance also provide explicit approximate sharpness constants. Numerical experiments show that WARPd compares favorably with specialized state-of-the-art methods and is ideally suited for solving large-scale problems. We also present a noise-blind variant based on a square-root LASSO decoder. Finally, we show how to unroll WARPd as neural networks. This approximation theory result provides lower bounds for stable and accurate neural networks for inverse problems and sheds light on architecture choices. Code and a gallery of examples are available online as a MATLAB package.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"315 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122111947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A General Non-Lipschitz Infimal Convolution Regularized Model: Lower Bound Theory and Algorithm 一般非lipschitz∞卷积正则化模型:下界理论与算法

SIAM J. Imaging Sci. Pub Date : 2022-08-31 DOI: 10.1137/20m1356634

Chunlin Wu, Xu-Yang Guo, Yiming Gao, Yunhua Xue

引用次数: 0

Multiscale Approach for Three-Dimensional Conformal Image Registration 三维保形图像配准的多尺度方法

SIAM J. Imaging Sci. Pub Date : 2022-08-23 DOI: 10.1137/21m1455929

Huan Han, Zhengping Wang, Yimin Zhang

引用次数: 3

A Spatial Color Compensation Model Using Saturation-Value Total Variation 一种基于饱和值总变差的空间色彩补偿模型

SIAM J. Imaging Sci. Pub Date : 2022-08-18 DOI: 10.1137/21m1453773

Wei Wang, Yu-Miao Yang, M. K. Ng

引用次数: 0

$L_1$-Norm Regularization for Short-and-Sparse Blind Deconvolution: Point Source Separability and Region Selection 短稀疏盲反卷积的$L_1$范数正则化:点源可分性和区域选择

SIAM J. Imaging Sci. Pub Date : 2022-08-16 DOI: 10.1137/21m144904x

Weixi Wang, Ji Li, Hui Ji

{"title":"$L_1$-Norm Regularization for Short-and-Sparse Blind Deconvolution: Point Source Separability and Region Selection","authors":"Weixi Wang, Ji Li, Hui Ji","doi":"10.1137/21m144904x","DOIUrl":"https://doi.org/10.1137/21m144904x","url":null,"abstract":". Blind deconvolution is about estimating both the convolution kernel and the latent signal from their 5 convolution. Many blind deconvolution problems have a short-and-sparse (SaS) structure, i.e . the 6 signal (or its gradient) is sparse and the kernel size is much smaller than the signal size. While ℓ 1 -norm 7 relating regularizations have been widely used for solving SaS blind deconvolution problems, the so- 8 called region/edge selection technique brings great empirical improvement to such ℓ 1 -norm relating 9 regularizations in image deblurring. The essence of region/edge selection is during an alternative 10 iterative scheme of SaS blind deconvolution, one estimates the kernel on an estimate of the latent 11 image with well-separated image edges instead of the one with the least fitting error. In this paper, 12 we first examines the validity and soundness of ℓ 1 -norm relating regularization in the setting of 1D 13 SaS blind deconvolution. The analysis reveals the importance of the separation of non-zero signal 14 entries toward the soundness of such a regularization. The studies laid out the foundation of region 15 selection technique, i.e ., during the iteration, an estimate of the latent image with well-separated 16 edges is a better candidate for estimating the kernel than the one with least fitting error. Based 17 on the studies conducted in this paper, an alternating iterative scheme with region selection model 18 is developed for SaS blind deconvolution, which is then applied on blind motion deblurring. The 19 experiments showed its effectiveness over many existing ℓ 1 -norm relating approaches. 20","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125198477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Joint reconstruction-segmentation on graphs 图上的联合重构分割

SIAM J. Imaging Sci. Pub Date : 2022-08-11 DOI: 10.1137/22M151546X

J. Budd, Y. Gennip, J. Latz, S. Parisotto, C. Schönlieb

{"title":"Joint reconstruction-segmentation on graphs","authors":"J. Budd, Y. Gennip, J. Latz, S. Parisotto, C. Schönlieb","doi":"10.1137/22M151546X","DOIUrl":"https://doi.org/10.1137/22M151546X","url":null,"abstract":"Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation methods, such as the Chan--Vese algorithm. In this paper, we present a method for joint reconstruction-segmentation using graph-based segmentation methods, which have been seeing increasing recent interest. Complications arise due to the large size of the matrices involved, and we show how these complications can be managed. We then analyse the convergence properties of our scheme. Finally, we apply this scheme to distorted versions of ``two cows'' images familiar from previous graph-based segmentation literature, first to a highly noised version and second to a blurred version, achieving highly accurate segmentations in both cases. We compare these results to those obtained by sequential reconstruction-segmentation approaches, finding that our method competes with, or even outperforms, those approaches in terms of reconstruction and segmentation accuracy.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114850156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Compressive Learning for Patch-Based Image Denoising 基于patch的图像去噪压缩学习

SIAM J. Imaging Sci. Pub Date : 2022-08-02 DOI: 10.1137/21m1459812

Hui Shi, Yann Traonmilin, Jean-François Aujol

引用次数: 6

Stability and Reconstruction of a Special Type of Anisotropic Conductivity in Magneto-Acoustic Tomography with Magnetic Induction 磁感应磁声层析成像中一种特殊类型的各向异性电导率的稳定性和重建

SIAM J. Imaging Sci. Pub Date : 2022-07-29 DOI: 10.1137/22m1512260

Niall Donlon, Romina Gaburro, S. Moskow, Isaac D. Woods

引用次数: 0

Separable Quaternion Matrix Factorization for Polarization Images 偏振图像的可分离四元数矩阵分解

SIAM J. Imaging Sci. Pub Date : 2022-07-28 DOI: 10.48550/arXiv.2207.14039

Junjun Pan, Michael K. Ng