{"title":"Tensor Robust Principal Component Analysis via Tensor Fibered Rank and ({boldsymbol{{l_p}}}) Minimization","authors":"Kaixin Gao, Zhenghai Huang","doi":"10.1137/22m1473236","DOIUrl":"https://doi.org/10.1137/22m1473236","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121370004","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}
{"title":"Nonlocal Perimeters and Curvature Flows on Graphs with Applications in Image Processing and High-Dimensional Data Classification","authors":"Imad El Bouchairi, A. Elmoataz, M. Fadili","doi":"10.1137/22m148598x","DOIUrl":"https://doi.org/10.1137/22m148598x","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121090920","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}
{"title":"Short Communication: Weak Sparse Superresolution is Well-Conditioned","authors":"Mathias Hockmann, Stefan Kunis","doi":"10.1137/22m1521353","DOIUrl":"https://doi.org/10.1137/22m1521353","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121674479","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}
{"title":"Stability for Finite Element Discretization of Some Inverse Parameter Problems from Internal Data: Application to Elastography","authors":"É. Bretin, Pierre Millien, Laurent Seppecher","doi":"10.1137/21m1428522","DOIUrl":"https://doi.org/10.1137/21m1428522","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131608054","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}
{"title":"On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces","authors":"Ž. Kereta, Bangti Jin","doi":"10.48550/arXiv.2302.05197","DOIUrl":"https://doi.org/10.48550/arXiv.2302.05197","url":null,"abstract":"In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and signal processing, etc. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularising property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"110 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120877600","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}
{"title":"Waveform Inversion with a Data Driven Estimate of the Internal Wave","authors":"L. Borcea, J. Garnier, A. Mamonov, J. Zimmerling","doi":"10.1137/22m1517342","DOIUrl":"https://doi.org/10.1137/22m1517342","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"4 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129216682","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}
{"title":"An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multiphase Image Segmentation","authors":"Chao Liu, Zhonghua Qiao, Qian Zhang","doi":"10.1137/22m1483645","DOIUrl":"https://doi.org/10.1137/22m1483645","url":null,"abstract":"","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129724976","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}
{"title":"Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation","authors":"M. Klibanov, Jingzhi Li, L. Nguyen, Zhipeng Yang","doi":"10.1137/22m1509837","DOIUrl":"https://doi.org/10.1137/22m1509837","url":null,"abstract":". An ( n + 1) − D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally conver- gent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Exten-sive numerical studies in the 2-D case are presented. Our are the source along an interval of a line and the data are only at a part of the boundary of the of is unlike the classical case of X-ray tomography when the runs all around and the are on the","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114521600","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}
É. Chouzenoux, Andres Contreras, J. Pesquet, Marion Savanier
{"title":"Convergence Results for Primal-Dual Algorithms in the Presence of Adjoint Mismatch","authors":"É. Chouzenoux, Andres Contreras, J. Pesquet, Marion Savanier","doi":"10.1137/22m1490223","DOIUrl":"https://doi.org/10.1137/22m1490223","url":null,"abstract":"Most optimization problems arising in imaging science involve high-dimensional linear operators and their adjoints. In the implementations of these operators, approximations may be introduced for various practical considerations (e.g., memory limitation, computational cost, convergence speed), leading to an adjoint mismatch . This occurs for the X-ray tomographic inverse problems found in Computed Tomography (CT), where the adjoint of the measurement operator (called projector) is often replaced by a surrogate operator. The resulting adjoint mismatch can jeopardize the convergence properties of iterative schemes used for image recovery. In this paper, we study the theoretical behavior of a panel of primal-dual proximal algorithms, which rely on forward-backward-(forward) splitting schemes, when an adjoint mismatch occurs. We analyze these algorithms by focusing on the resolution of possibly non-smooth convex penalized minimization problems in an infinite-dimensional setting. By using tools from fixed point theory, we show that they can solve monotone inclusions that go beyond minimization problems. Such findings indicate these algorithms can be seen as a generalization of classical primal-dual formulations. The applicability of our findings are also demonstrated through two numerical experiments in the context of CT image reconstruction.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124333101","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}