Nonconvex Penalized Regularization for Robust Sparse Recovery in the Presence of S\alpha S Noise
Nonconvex penalties have recently received considerable attention in sparse recovery based on Gaussian assumptions. However, many sparse recovery problems occur in the presence of impulsive noises. This paper is concerned with the analysis and comparison of different sparsity-inducing penalties for...
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Veröffentlicht in: | IEEE access 2018-01, Vol.6, p.25474-25485 |
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description | Nonconvex penalties have recently received considerable attention in sparse recovery based on Gaussian assumptions. However, many sparse recovery problems occur in the presence of impulsive noises. This paper is concerned with the analysis and comparison of different sparsity-inducing penalties for L_{1} -loss function-based robust sparse recovery. To solve these nonconvex and nonsmooth optimization problems, we use the alternating direction method of multipliers framework to split this difficult problem into tractable sub-problems in combination with corresponding iterative proximal operators. This paper employs different nonconvex penalties and compares the performances, advantages, and properties and provides guidance for the choice of the best regularizer for sparse recovery with different levels of impulsive noise. Experimental results indicate that convex lasso ( L_{1} -norm) penalty is more effective for the suppression of highly impulsive noise than nonconvex penalties, while the nonconvex penalties show the potential to improve the performance in low and medium level noise. Moreover, among these nonconvex penalties, L_{p} norm can often obtain better recovery performance. |
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However, many sparse recovery problems occur in the presence of impulsive noises. This paper is concerned with the analysis and comparison of different sparsity-inducing penalties for <inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-loss function-based robust sparse recovery. To solve these nonconvex and nonsmooth optimization problems, we use the alternating direction method of multipliers framework to split this difficult problem into tractable sub-problems in combination with corresponding iterative proximal operators. This paper employs different nonconvex penalties and compares the performances, advantages, and properties and provides guidance for the choice of the best regularizer for sparse recovery with different levels of impulsive noise. Experimental results indicate that convex lasso (<inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-norm) penalty is more effective for the suppression of highly impulsive noise than nonconvex penalties, while the nonconvex penalties show the potential to improve the performance in low and medium level noise. Moreover, among these nonconvex penalties, <inline-formula> <tex-math notation="LaTeX">L_{p} </tex-math></inline-formula> norm can often obtain better recovery performance.]]></description><identifier>ISSN: 2169-3536</identifier><identifier>EISSN: 2169-3536</identifier><identifier>DOI: 10.1109/ACCESS.2018.2830771</identifier><identifier>CODEN: IAECCG</identifier><language>eng</language><publisher>IEEE</publisher><subject>alternating direction method of multipliers (ADMM) ; Convex functions ; Image restoration ; impulsive noise ; Iterative algorithms ; Noise measurement ; Nonconvex penalties ; Optimization ; robust sparse recovery ; Robustness ; Telecommunications</subject><ispartof>IEEE access, 2018-01, Vol.6, p.25474-25485</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c335t-3ed07b567db9ed9a8c5d461aa7f3cecca0ba20a636f67fb7c5dd8665573892663</citedby><cites>FETCH-LOGICAL-c335t-3ed07b567db9ed9a8c5d461aa7f3cecca0ba20a636f67fb7c5dd8665573892663</cites><orcidid>0000-0003-1379-9301 ; 0000-0003-0073-1965 ; 0000-0003-3888-2881</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8351921$$EHTML$$P50$$Gieee$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,864,2102,27633,27924,27925,54933</link.rule.ids></links><search><creatorcontrib>Li, Yunyi</creatorcontrib><creatorcontrib>Lin, Yun</creatorcontrib><creatorcontrib>Cheng, Xiefeng</creatorcontrib><creatorcontrib>Xiao, Zhuolei</creatorcontrib><creatorcontrib>Shu, Feng</creatorcontrib><creatorcontrib>Gui, Guan</creatorcontrib><title>Nonconvex Penalized Regularization for Robust Sparse Recovery in the Presence of S\alpha S Noise</title><title>IEEE access</title><addtitle>Access</addtitle><description><![CDATA[Nonconvex penalties have recently received considerable attention in sparse recovery based on Gaussian assumptions. However, many sparse recovery problems occur in the presence of impulsive noises. This paper is concerned with the analysis and comparison of different sparsity-inducing penalties for <inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-loss function-based robust sparse recovery. To solve these nonconvex and nonsmooth optimization problems, we use the alternating direction method of multipliers framework to split this difficult problem into tractable sub-problems in combination with corresponding iterative proximal operators. This paper employs different nonconvex penalties and compares the performances, advantages, and properties and provides guidance for the choice of the best regularizer for sparse recovery with different levels of impulsive noise. Experimental results indicate that convex lasso (<inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-norm) penalty is more effective for the suppression of highly impulsive noise than nonconvex penalties, while the nonconvex penalties show the potential to improve the performance in low and medium level noise. Moreover, among these nonconvex penalties, <inline-formula> <tex-math notation="LaTeX">L_{p} </tex-math></inline-formula> norm can often obtain better recovery performance.]]></description><subject>alternating direction method of multipliers (ADMM)</subject><subject>Convex functions</subject><subject>Image restoration</subject><subject>impulsive noise</subject><subject>Iterative algorithms</subject><subject>Noise measurement</subject><subject>Nonconvex penalties</subject><subject>Optimization</subject><subject>robust sparse recovery</subject><subject>Robustness</subject><subject>Telecommunications</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNkNtKJDEQhptlFxT1CbzJC8yYdE1OlzJ4AnHF1ruFWElXNNLbGZJWVp_edkfEuqmiqv7v4muaQ8GXQnB7dLxen3TdsuXCLFsDXGvxo9lthbILkKB-fpt3moNan_hcZl5JvdvcX-Ux5PGF_rFrGnFIb9SzG3p4HrCkN5xSHlnMhd1k_1wn1m2wVJofQn6h8srSyKZHYteFKo2BWI6s-4PD5hFZx65yqrTf_Io4VDr47HvN3enJ7fp8cfn77GJ9fLkIAHJaAPVce6l07y31Fk2Q_UoJRB0hUAjIPbYcFaiodPR6PvdGKSk1GNsqBXvNxZbbZ3xym5L-Ynl1GZP7v8jlwWGZUhjIeQqghfERga-8ARMFSbJW-ZUFhXFmwZYVSq61UPziCe4-nLutc_fh3H06n1OH21Qioq-EASlsK-Ad-tF-rw</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>Li, Yunyi</creator><creator>Lin, Yun</creator><creator>Cheng, Xiefeng</creator><creator>Xiao, Zhuolei</creator><creator>Shu, Feng</creator><creator>Gui, Guan</creator><general>IEEE</general><scope>97E</scope><scope>ESBDL</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-1379-9301</orcidid><orcidid>https://orcid.org/0000-0003-0073-1965</orcidid><orcidid>https://orcid.org/0000-0003-3888-2881</orcidid></search><sort><creationdate>20180101</creationdate><title>Nonconvex Penalized Regularization for Robust Sparse Recovery in the Presence of S\alpha S Noise</title><author>Li, Yunyi ; Lin, Yun ; Cheng, Xiefeng ; Xiao, Zhuolei ; Shu, Feng ; Gui, Guan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-3ed07b567db9ed9a8c5d461aa7f3cecca0ba20a636f67fb7c5dd8665573892663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>alternating direction method of multipliers (ADMM)</topic><topic>Convex functions</topic><topic>Image restoration</topic><topic>impulsive noise</topic><topic>Iterative algorithms</topic><topic>Noise measurement</topic><topic>Nonconvex penalties</topic><topic>Optimization</topic><topic>robust sparse recovery</topic><topic>Robustness</topic><topic>Telecommunications</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Yunyi</creatorcontrib><creatorcontrib>Lin, Yun</creatorcontrib><creatorcontrib>Cheng, Xiefeng</creatorcontrib><creatorcontrib>Xiao, Zhuolei</creatorcontrib><creatorcontrib>Shu, Feng</creatorcontrib><creatorcontrib>Gui, Guan</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE Open Access Journals</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>IEEE access</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Yunyi</au><au>Lin, Yun</au><au>Cheng, Xiefeng</au><au>Xiao, Zhuolei</au><au>Shu, Feng</au><au>Gui, Guan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonconvex Penalized Regularization for Robust Sparse Recovery in the Presence of S\alpha S Noise</atitle><jtitle>IEEE access</jtitle><stitle>Access</stitle><date>2018-01-01</date><risdate>2018</risdate><volume>6</volume><spage>25474</spage><epage>25485</epage><pages>25474-25485</pages><issn>2169-3536</issn><eissn>2169-3536</eissn><coden>IAECCG</coden><abstract><![CDATA[Nonconvex penalties have recently received considerable attention in sparse recovery based on Gaussian assumptions. However, many sparse recovery problems occur in the presence of impulsive noises. This paper is concerned with the analysis and comparison of different sparsity-inducing penalties for <inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-loss function-based robust sparse recovery. To solve these nonconvex and nonsmooth optimization problems, we use the alternating direction method of multipliers framework to split this difficult problem into tractable sub-problems in combination with corresponding iterative proximal operators. This paper employs different nonconvex penalties and compares the performances, advantages, and properties and provides guidance for the choice of the best regularizer for sparse recovery with different levels of impulsive noise. Experimental results indicate that convex lasso (<inline-formula> <tex-math notation="LaTeX">L_{1} </tex-math></inline-formula>-norm) penalty is more effective for the suppression of highly impulsive noise than nonconvex penalties, while the nonconvex penalties show the potential to improve the performance in low and medium level noise. Moreover, among these nonconvex penalties, <inline-formula> <tex-math notation="LaTeX">L_{p} </tex-math></inline-formula> norm can often obtain better recovery performance.]]></abstract><pub>IEEE</pub><doi>10.1109/ACCESS.2018.2830771</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0003-1379-9301</orcidid><orcidid>https://orcid.org/0000-0003-0073-1965</orcidid><orcidid>https://orcid.org/0000-0003-3888-2881</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | alternating direction method of multipliers (ADMM) Convex functions Image restoration impulsive noise Iterative algorithms Noise measurement Nonconvex penalties Optimization robust sparse recovery Robustness Telecommunications |
title | Nonconvex Penalized Regularization for Robust Sparse Recovery in the Presence of S\alpha S Noise |
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