Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis
Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a...
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| Veröffentlicht in: | IEEE transactions on information theory 2024-11, p.1-1 |
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| creator | He, Zhuohang Ma, Junjie Yuan, Xiaojun |
| description | Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations. |
| doi_str_mv | 10.1109/TIT.2024.3509476 |
| format | Article |
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In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations.</description><subject>approximate message passing</subject><subject>Approximation algorithms</subject><subject>Bayes methods</subject><subject>compressed sensing</subject><subject>Convergence</subject><subject>Face recognition</subject><subject>Heuristic algorithms</subject><subject>Inference algorithms</subject><subject>low-rank matrix denoising</subject><subject>Message passing</subject><subject>Noise measurement</subject><subject>phase transition</subject><subject>Principal component analysis</subject><subject>random matrix theory</subject><subject>Robust PCA</subject><subject>singular value thresholding</subject><subject>Sparse matrices</subject><subject>state evolution</subject><issn>0018-9448</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFisFqwkAURWehUKvuu3DxfsB0Jk4a012wii4Ekexl1Gf6SjIT5o1CoB_fINKtq8u55wjxpmSklMzei00RxTLW0SyRmU4_emIgpZpPM63nL-KV-adDnah4IH43dePdDc9QXP3RwRaZTYmwM8xkS7g4DwvXNd1PN4S9O145wM6TPVFjqrt0Fm2A3JqqZeJPyKvSeQrfNXwhU2nB2DPk3NZNcIFO_-VI9C-mYhw_digmq2WxWE8JEQ-Np9r49qBkmsYqyWZP9B_8KU7S</recordid><startdate>20241129</startdate><enddate>20241129</enddate><creator>He, Zhuohang</creator><creator>Ma, Junjie</creator><creator>Yuan, Xiaojun</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><orcidid>https://orcid.org/0000-0002-0433-6535</orcidid><orcidid>https://orcid.org/0000-0003-1263-5006</orcidid></search><sort><creationdate>20241129</creationdate><title>Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis</title><author>He, Zhuohang ; Ma, Junjie ; Yuan, Xiaojun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-ieee_primary_107721593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>approximate message passing</topic><topic>Approximation algorithms</topic><topic>Bayes methods</topic><topic>compressed sensing</topic><topic>Convergence</topic><topic>Face recognition</topic><topic>Heuristic algorithms</topic><topic>Inference algorithms</topic><topic>low-rank matrix denoising</topic><topic>Message passing</topic><topic>Noise measurement</topic><topic>phase transition</topic><topic>Principal component analysis</topic><topic>random matrix theory</topic><topic>Robust PCA</topic><topic>singular value thresholding</topic><topic>Sparse matrices</topic><topic>state evolution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>He, Zhuohang</creatorcontrib><creatorcontrib>Ma, Junjie</creatorcontrib><creatorcontrib>Yuan, Xiaojun</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>He, Zhuohang</au><au>Ma, Junjie</au><au>Yuan, Xiaojun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2024-11-29</date><risdate>2024</risdate><spage>1</spage><epage>1</epage><pages>1-1</pages><issn>0018-9448</issn><coden>IETTAW</coden><abstract>Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. 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| subjects | approximate message passing Approximation algorithms Bayes methods compressed sensing Convergence Face recognition Heuristic algorithms Inference algorithms low-rank matrix denoising Message passing Noise measurement phase transition Principal component analysis random matrix theory Robust PCA singular value thresholding Sparse matrices state evolution |
| title | Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis |
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