SIAM J. Imaging Sci.最新文献_第9页

A unifying framework for n-dimensional quasi-conformal mappings n维拟共形映射的统一框架

SIAM J. Imaging Sci. Pub Date : 2021-10-20 DOI: 10.1137/21M1457497

Daoping Zhang, G. Choi, Jianping Zhang, L. Lui

引用次数: 4

Adaptive and Implicit Regularization for Matrix Completion 矩阵补全的自适应隐式正则化

SIAM J. Imaging Sci. Pub Date : 2021-10-12 DOI: 10.1137/22M1489228

Zhemin Li, Tao Sun, Hongxia Wang, Bao Wang

引用次数: 3

Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory 作为具有互补性约束的数学程序的双层成像学习问题:重新表述和理论

SIAM J. Imaging Sci. Pub Date : 2021-10-05 DOI: 10.1137/21m1450744

J. C. Reyes

{"title":"Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory","authors":"J. C. Reyes","doi":"10.1137/21m1450744","DOIUrl":"https://doi.org/10.1137/21m1450744","url":null,"abstract":"We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of the primal-dual reformulation of the lower-level problem and introducing suitable auxiliar variables, we are able to reformulate the original bilevel problems as Mathematical Programs with Complementarity Constraints (MPCC). For the latter, we prove tight constraint qualification conditions (MPCC-RCPLD and partial MPCC-LICQ) and derive Mordukhovich (M-) and Strong (S-) stationarity conditions. The stationarity systems for the MPCC turn also into stationarity conditions for the original formulation. Second-order sufficient optimality conditions are derived as well, together with a local uniqueness result for stationary points. The proposed reformulation may be extended to problems in function spaces, leading to MPCC's with constraints on the gradient of the state. The MPCC reformulation also leads to the efficient use of available large-scale nonlinear programming solvers, as shown in a companion paper, where different imaging applications are studied.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124236650","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

Linear convergence of randomized Kaczmarz method for solving complex-valued phaseless equations 求解复值无相方程的随机Kaczmarz方法的线性收敛性

SIAM J. Imaging Sci. Pub Date : 2021-09-24 DOI: 10.1137/21m1450537

Meng-zhi Huang, Yang Wang

引用次数: 9

Convergence Results in Image Interpolation With the Continuous SSIM 连续SSIM图像插值的收敛性

SIAM J. Imaging Sci. Pub Date : 2021-08-09 DOI: 10.1137/22M147637X

F. Marchetti, G. Santin

{"title":"Convergence Results in Image Interpolation With the Continuous SSIM","authors":"F. Marchetti, G. Santin","doi":"10.1137/22M147637X","DOIUrl":"https://doi.org/10.1137/22M147637X","url":null,"abstract":"Assessing the similarity of two images is a complex task that attracts significant efforts in the image processing community. The widely used Structural Similarity Index Measure (SSIM) addresses this problem by quantifying a perceptual structural similarity. In this paper we consider a recently introduced continuous SSIM (cSSIM), which allows one to analyze sequences of images of increasingly fine resolutions, and further extend the definition of the index to encompass the locally weighted version that is used in practice. For both the local and the global versions, we prove that the continuous index includes the classical SSIM as a special case, and we provide a precise connection between image similarity measured by the cSSIM and by the $L_2$ norm. Using this connection, we derive bounds on the cSSIM by means of bounds on the $L_2$ error, and we even prove that the two error measures are equivalent in certain circumstances. We exploit these results to obtain precise rates of convergence with respect to the cSSIM for several concrete image interpolation methods, and we further validate these findings by different numerical experiments. This newly established connection paves the way to obtain novel insights into the features and limitations of the SSIM, including on the effect of the local weighted window on the index performances.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124289636","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

Distributed Stochastic Inertial-Accelerated Methods with Delayed Derivatives for Nonconvex Problems 非凸问题的延迟导数分布随机惯性加速方法

SIAM J. Imaging Sci. Pub Date : 2021-07-24 DOI: 10.1137/21m1435719

Yangyang Xu, Yibo Xu, Yonggui Yan, Jiewei Chen

{"title":"Distributed Stochastic Inertial-Accelerated Methods with Delayed Derivatives for Nonconvex Problems","authors":"Yangyang Xu, Yibo Xu, Yonggui Yan, Jiewei Chen","doi":"10.1137/21m1435719","DOIUrl":"https://doi.org/10.1137/21m1435719","url":null,"abstract":"Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little exploration has been made on applying a certain acceleration technique to a stochastic subgradient method (SsGM) for nonsmooth nonconvex problems. In addition, few efforts have been made to analyze an (accelerated) SsGM with delayed derivatives. The information delay naturally happens in a distributed system, where computing workers do not coordinate with each other. In this paper, we propose an inertial proximal SsGM for solving nonsmooth nonconvex stochastic optimization problems. The proposed method can have guaranteed convergence even with delayed derivative information in a distributed environment. Convergence rate results are established to three classes of nonconvex problems: weakly-convex nonsmooth problems with a convex regularizer, composite nonconvex problems with a nonsmooth convex regularizer, and smooth nonconvex problems. For each problem class, the convergence rate is $O(1/K^{frac{1}{2}})$ in the expected value of the gradient norm square, for $K$ iterations. In a distributed environment, the convergence rate of the proposed method will be slowed down by the information delay. Nevertheless, the slow-down effect will decay with the number of iterations for the latter two problem classes. We test the proposed method on three applications. The numerical results clearly demonstrate the advantages of using the inertial-based acceleration. Furthermore, we observe higher parallelization speed-up in asynchronous updates over the synchronous counterpart, though the former uses delayed derivatives. Our source code is released at https://github.com/RPI-OPT/Inertial-SsGM","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133409893","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

Optimality Conditions for Bilevel Imaging Learning Problems with Total Variation Regularization 全变分正则化双层成像学习问题的最优性条件

SIAM J. Imaging Sci. Pub Date : 2021-07-16 DOI: 10.1137/21m143412x

J. C. Reyes, David Villacis

引用次数: 5

Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields 提升拉格朗日松弛中的凸共轭:连续马尔可夫随机场的一种可处理方法

SIAM J. Imaging Sci. Pub Date : 2021-07-13 DOI: 10.1137/21m1433241

Hartmut Bauermeister, Emanuel Laude, T. Möllenhoff, M. Moeller, D. Cremers

{"title":"Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields","authors":"Hartmut Bauermeister, Emanuel Laude, T. Möllenhoff, M. Moeller, D. Cremers","doi":"10.1137/21m1433241","DOIUrl":"https://doi.org/10.1137/21m1433241","url":null,"abstract":"Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state spaces. To eliminate such gaps, this paper considers a reformulation of the original nonconvex task in the space of measures. This infinite-dimensional reformulation is then approximated by a semi-infinite one, which is obtained via a piecewise polynomial discretization in the dual. We provide a geometric intuition behind the primal problem induced by the dual discretization and draw connections to optimization over moment spaces. In contrast to existing discretizations which suffer from a grid bias, we show that a piecewise polynomial discretization better preserves the continuous nature of our problem. Invoking results from optimal transport theory and convex algebraic geometry we reduce the semi-infinite program to a finite one and provide a practical implementation based on semidefinite programming. We show, experimentally and in theory, that the approach successfully reduces the duality gap. To showcase the scalability of our approach, we apply it to the stereo matching problem between two images.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"313 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128742199","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: 7

A Splitting Scheme for Flip-Free Distortion Energies 一种无翻转畸变能量的分裂方案

SIAM J. Imaging Sci. Pub Date : 2021-07-12 DOI: 10.1137/21M1433058

Oded Stein, Jiajin Li, J. Solomon

引用次数: 6

SISAL Revisited 剑麻Revisited

SIAM J. Imaging Sci. Pub Date : 2021-07-01 DOI: 10.1137/21m1430613

Chu-Hsiang Huang, Mingjie Shao, Wing-Kin Ma, A. M. So

{"title":"SISAL Revisited","authors":"Chu-Hsiang Huang, Mingjie Shao, Wing-Kin Ma, A. M. So","doi":"10.1137/21m1430613","DOIUrl":"https://doi.org/10.1137/21m1430613","url":null,"abstract":"Simplex identification via split augmented Lagrangian (SISAL) is a popularly-used algorithm in 4 blind unmixing of hyperspectral images. Developed by José M. Bioucas-Dias in 2009, the algorithm 5 is fundamentally relevant to tackling simplex-structured matrix factorization, and by extension, non6 negative matrix factorization, which have many applications under their umbrellas. In this article, we 7 revisit SISAL and provide new meanings to this quintessential algorithm. The formulation of SISAL 8 was motivated from a geometric perspective, with no noise. We show that SISAL can be explained 9 as an approximation scheme from a probabilistic simplex component analysis framework, which is 10 statistical and is principally more powerful in accommodating the presence of noise. The algorithm 11 for SISAL was designed based on a successive convex approximation method, with a focus on practical 12 utility. It was not known, by analyses, whether the SISAL algorithm has any kind of guarantee 13 of convergence to a stationary point. By establishing associations between the SISAL algorithm 14 and a line-search-based proximal gradient method, we confirm that SISAL can indeed guarantee 15 convergence to a stationary point. Our re-explanation of SISAL also reveals new formulations and 16 algorithms. The performance of these new possibilities is demonstrated by numerical experiments. 17","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115397627","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: 2