SIAM Journal on Imaging Sciences最新文献_第3页

Training Adaptive Reconstruction Networks for Blind Inverse Problems 为盲反问题训练自适应重构网络

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-21 DOI: 10.1137/23m1545628

Alban Gossard, Pierre Weiss

引用次数: 0

Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on Surfaces 用于曲面图像去噪的非 Lipschitz 变分模型及其迭代加权最小二乘法算法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-20 DOI: 10.1137/23m159439x

Yuan Liu, Chunlin Wu, Chao Zeng

引用次数: 0

Riesz Feature Representation: Scale Equivariant Scattering Network for Classification Tasks 里兹特征表示：用于分类任务的尺度等变散射网络

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-20 DOI: 10.1137/23m1584836

Tin Barisin, Jesus Angulo, Katja Schladitz, Claudia Redenbach

{"title":"Riesz Feature Representation: Scale Equivariant Scattering Network for Classification Tasks","authors":"Tin Barisin, Jesus Angulo, Katja Schladitz, Claudia Redenbach","doi":"10.1137/23m1584836","DOIUrl":"https://doi.org/10.1137/23m1584836","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1284-1313, June 2024. Abstract. Scattering networks yield powerful and robust hierarchical image descriptors which do not require lengthy training and which work well with very few training data. However, they rely on sampling the scale dimension. Hence, they become sensitive to scale variations and are unable to generalize to unseen scales. In this work, we define an alternative feature representation based on the Riesz transform. We detail and analyze the mathematical foundations behind this representation. In particular, it inherits scale equivariance from the Riesz transform and completely avoids sampling of the scale dimension. Additionally, the number of features in the representation is reduced by a factor four compared to scattering networks. Nevertheless, our representation performs comparably well for texture classification with an interesting addition: scale equivariance. Our method yields very good performance when dealing with scales outside of those covered by the training dataset. The usefulness of the equivariance property is demonstrated on the digit classification task, where accuracy remains stable even for scales four times larger than the one chosen for training. As a second example, we consider classification of textures. Finally, we show how this representation can be used to build hybrid deep learning methods that are more stable to scale variations than standard deep networks.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"111 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Marginal Likelihood Estimation in Semiblind Image Deconvolution: A Stochastic Approximation Approach 半盲图像解卷积中的边际似然估计：随机逼近法

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-19 DOI: 10.1137/23m1584496

Charlesquin Kemajou Mbakam, Marcelo Pereyra, Jean-François Giovannelli

{"title":"Marginal Likelihood Estimation in Semiblind Image Deconvolution: A Stochastic Approximation Approach","authors":"Charlesquin Kemajou Mbakam, Marcelo Pereyra, Jean-François Giovannelli","doi":"10.1137/23m1584496","DOIUrl":"https://doi.org/10.1137/23m1584496","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1206-1254, June 2024. Abstract.This paper presents a novel stochastic optimization methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed optimization approach automatically calibrates the parameters of the blur model by maximum marginal likelihood estimation, followed by (non-blind) image deconvolution by maximum a posteriori estimation conditionally to the estimated model parameters. In addition to the blur model, the proposed approach also automatically calibrates the noise level as well as any regularization parameters. The marginal likelihood of the blur, noise, and regularization parameters is generally computationally intractable, as it requires calculating several integrals over the entire solution space. Our approach addresses this difficulty by using a stochastic approximation proximal gradient optimization scheme, which iteratively solves such integrals by using a Moreau–Yosida regularized unadjusted Langevin Markov chain Monte Carlo algorithm. This optimization strategy can be easily and efficiently applied to any model that is log-concave and by using the same gradient and proximal operators that are required to compute the maximum a posteriori solution by convex optimization. We provide convergence guarantees for the proposed optimization scheme under realistic and easily verifiable conditions and subsequently demonstrate the effectiveness of the approach with a series of deconvolution experiments and comparisons with alternative strategies from the state of the art","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"8 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stable Local-Smooth Principal Component Pursuit 稳定的局部平滑主成分搜索

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-17 DOI: 10.1137/23m1580164

Jiangjun Peng, Hailin Wang, Xiangyong Cao, Xixi Jia, Hongying Zhang, Deyu Meng

{"title":"Stable Local-Smooth Principal Component Pursuit","authors":"Jiangjun Peng, Hailin Wang, Xiangyong Cao, Xixi Jia, Hongying Zhang, Deyu Meng","doi":"10.1137/23m1580164","DOIUrl":"https://doi.org/10.1137/23m1580164","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1182-1205, June 2024. Abstract.Recently, the CTV-RPCA model proposed the first recoverable theory for separating low-rank and local-smooth matrices and sparse matrices based on the correlated total variation (CTV) regularizer. However, the CTV-RPCA model ignores the influence of noise, which makes the model unable to effectively extract low-rank and local-smooth principal components under noisy circumstances. To alleviate this issue, this article extends the CTV-RPCA model by considering the influence of noise and proposes two robust models with parameter adaptive adjustment, i.e., Stable Principal Component Pursuit based on CTV (CTV-SPCP) and Square Root Principal Component Pursuit based on CTV (CTV-[math]). Furthermore, we present a statistical recoverable error bound for the proposed models, which allows us to know the relationship between the solution of the proposed models and the ground-truth. It is worth mentioning that, in the absence of noise, our theory degenerates back to the exact recoverable theory of the CTV-RPCA model. Finally, we develop the effective algorithms with the strict convergence guarantees. Extensive experiments adequately validate the theoretical assertions and also demonstrate the superiority of the proposed models over many state-of-the-art methods on various typical applications, including video foreground extraction, multispectral image denoising, and hyperspectral image denoising. The source code is released at https://github.com/andrew-pengjj/CTV-SPCP.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"72 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Extrapolated Plug-and-Play Three-Operator Splitting Methods for Nonconvex Optimization with Applications to Image Restoration 用于非凸优化的外推即插即用三操作器分割方法及其在图像复原中的应用

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-13 DOI: 10.1137/23m1611166

Zhongming Wu, Chaoyan Huang, Tieyong Zeng

{"title":"Extrapolated Plug-and-Play Three-Operator Splitting Methods for Nonconvex Optimization with Applications to Image Restoration","authors":"Zhongming Wu, Chaoyan Huang, Tieyong Zeng","doi":"10.1137/23m1611166","DOIUrl":"https://doi.org/10.1137/23m1611166","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1145-1181, June 2024. Abstract.This paper investigates the convergence properties and applications of the three-operator splitting method, also known as the Davis–Yin splitting (DYS) method, integrated with extrapolation and plug-and-play (PnP) denoiser within a nonconvex framework. We first propose an extrapolated DYS method to effectively solve a class of structural nonconvex optimization problems that involve minimizing the sum of three possibly nonconvex functions. Our approach provides an algorithmic framework that encompasses both extrapolated forward–backward splitting and extrapolated Douglas–Rachford splitting methods. To establish the convergence of the proposed method, we rigorously analyze its behavior based on the Kurdyka–Łojasiewicz property, subject to some tight parameter conditions. Moreover, we introduce two extrapolated PnP-DYS methods with convergence guarantee, where the traditional regularization step is replaced by a gradient step–based denoiser. This denoiser is designed using a differentiable neural network and can be reformulated as the proximal operator of a specific nonconvex functional. We conduct extensive experiments on image deblurring and image superresolution problems, where our numerical results showcase the advantage of the extrapolation strategy and the superior performance of the learning-based model that incorporates the PnP denoiser in terms of achieving high-quality recovery images.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"58 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic Variance Reduced Gradient for Affine Rank Minimization Problem 仿等级最小化问题的随机方差降低梯度

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-04 DOI: 10.1137/23m1555387

Ningning Han, Juan Nie, Jian Lu, Michael K. Ng

引用次数: 0

Accelerated Bayesian Imaging by Relaxed Proximal-Point Langevin Sampling 通过松弛近端点朗文采样加速贝叶斯成像

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-06-03 DOI: 10.1137/23m1594832

Teresa Klatzer, Paul Dobson, Yoann Altmann, Marcelo Pereyra, Jesus Maria Sanz-Serna, Konstantinos C. Zygalakis

{"title":"Accelerated Bayesian Imaging by Relaxed Proximal-Point Langevin Sampling","authors":"Teresa Klatzer, Paul Dobson, Yoann Altmann, Marcelo Pereyra, Jesus Maria Sanz-Serna, Konstantinos C. Zygalakis","doi":"10.1137/23m1594832","DOIUrl":"https://doi.org/10.1137/23m1594832","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1078-1117, June 2024. Abstract.This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed proximal-point iteration that admits two complementary interpretations. For models that are smooth or regularized by Moreau–Yosida smoothing, the algorithm is equivalent to an implicit midpoint discretization of an overdamped Langevin diffusion targeting the posterior distribution of interest. This discretization is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is [math]-strongly log-concave (i.e., requiring in the order of [math] iterations to converge, similar to accelerated optimization schemes), comparing favorably to Pereyra, Vargas Mieles, and Zygalakis [SIAM J. Imaging Sci., 13 (2020), pp. 905–935], which is only provably accelerated for Gaussian targets and has bias. For models that are not smooth, the algorithm is equivalent to a Leimkuhler–Matthews discretization of a Langevin diffusion targeting a Moreau–Yosida approximation of the posterior distribution of interest and hence achieves a significantly lower bias than conventional unadjusted Langevin strategies based on the Euler–Maruyama discretization. For targets that are [math]-strongly log-concave, the provided nonasymptotic convergence analysis also identifies the optimal time step, which maximizes the convergence speed. The proposed methodology is demonstrated through a range of experiments related to image deconvolution with Gaussian and Poisson noise with assumption-driven and data-driven convex priors. Source codes for the numerical experiments of this paper are available from https://github.com/MI2G/accelerated-langevin-imla.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"17 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Total Generalized Variation on a Tree 一棵树上的总体变化

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-05-30 DOI: 10.1137/23m1556915

Muhamed Kuric, Jan Ahmetspahic, Thomas Pock

{"title":"Total Generalized Variation on a Tree","authors":"Muhamed Kuric, Jan Ahmetspahic, Thomas Pock","doi":"10.1137/23m1556915","DOIUrl":"https://doi.org/10.1137/23m1556915","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1040-1077, June 2024. Abstract.We consider a class of optimization problems defined over trees with unary cost terms and shifted pairwise cost terms. These problems arise when considering block coordinate descent (BCD) approaches for solving inverse problems with total generalized variation (TGV) regularizers or their nonconvex generalizations. We introduce a linear-time reduction that transforms the shifted problems into their nonshifted counterparts. However, combining existing continuous dynamic programming (DP) algorithms with the reduction does not lead to BCD iterations that compute TGV-like solutions. This problem can be overcome by considering a box-constrained modification of the subproblems or smoothing the cost terms of the TGV regularized problem. The former leads to shifted and box-constrained subproblems, for which we propose a linear-time reduction to their unconstrained counterpart. The latter naturally leads to problems with smooth unary and pairwise cost terms. With this in mind, we propose two novel continuous DP algorithms that can solve (convex and nonconvex) problems with piecewise quadratic unary and pairwise cost terms. We prove that the algorithm for the convex case has quadratic worst-case time and memory complexity, while the algorithm for the nonconvex case has exponential time and memory complexity, but works well in practice for smooth truncated total variation pairwise costs. Finally, we demonstrate the applicability of the proposed algorithms for solving inverse problems with first-order and higher-order regularizers.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"58 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Imaging with Thermal Noise Induced Currents 利用热噪声诱导电流成像

IF 2.1 3区数学

SIAM Journal on Imaging Sciences Pub Date : 2024-05-21 DOI: 10.1137/23m1571630

Trent DeGiovanni, Fernando Guevara Vasquez, China Mauck

引用次数: 0