Iteratively reweighted algorithm for signals recovery with coherent tight frame
We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A sati...
Gespeichert in:
| Veröffentlicht in: | Mathematical methods in the applied sciences 2018-09, Vol.41 (14), p.5481-5492 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 5492 |
|---|---|
| container_issue | 14 |
| container_start_page | 5481 |
| container_title | Mathematical methods in the applied sciences |
| container_volume | 41 |
| creator | Bi, Ning Liang, Kaihao |
| description | We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a |
| doi_str_mv | 10.1002/mma.5091 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2083586240</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2083586240</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2931-be9e30a28cff8575505b0d0d65cb533fc6a8d1edfeacd31cc690dcb2a54edf493</originalsourceid><addsrcrecordid>eNp10E1rwzAMBmAzNljXDfYTDLvskk624zQ-lrKPQksv29k4ttymJE3nuC3590vWXXcSSI-EeAl5ZDBhAPylrs1EgmJXZMRAqYSl0-yajIBNIUk5S2_JXdvuACBnjI_IehExmFiesOpowDOWm21ER021aUIZtzX1TaBtudmbqu2BbU4YOnruR9Q2Wwy4jzQOS9QHU-M9ufG9xIe_OiZfb6-f849kuX5fzGfLxHIlWFKgQgGG59b7XE6lBFmAA5dJW0ghvM1M7hg6j8Y6wazNFDhbcCPTvpkqMSZPl7uH0HwfsY161xzD8KTmkAuZZzyFXj1flA1N2wb0-hDK2oROM9BDXLqPSw9x9TS50HNZYfev06vV7Nf_AAEDbVg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2083586240</pqid></control><display><type>article</type><title>Iteratively reweighted algorithm for signals recovery with coherent tight frame</title><source>Wiley Online Library</source><creator>Bi, Ning ; Liang, Kaihao</creator><creatorcontrib>Bi, Ning ; Liang, Kaihao</creatorcontrib><description>We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.5091</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Algorithms ; compressed sensing ; Discrete cosine transform ; D‐RIP ; Fourier transforms ; iteratively reweighted method ; sufficient D‐NSP ; tight frame ; Wavelet analysis</subject><ispartof>Mathematical methods in the applied sciences, 2018-09, Vol.41 (14), p.5481-5492</ispartof><rights>Copyright © 2018 John Wiley & Sons, Ltd.</rights><rights>2018 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2931-be9e30a28cff8575505b0d0d65cb533fc6a8d1edfeacd31cc690dcb2a54edf493</citedby><cites>FETCH-LOGICAL-c2931-be9e30a28cff8575505b0d0d65cb533fc6a8d1edfeacd31cc690dcb2a54edf493</cites><orcidid>0000-0002-3000-7137</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.5091$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.5091$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Bi, Ning</creatorcontrib><creatorcontrib>Liang, Kaihao</creatorcontrib><title>Iteratively reweighted algorithm for signals recovery with coherent tight frame</title><title>Mathematical methods in the applied sciences</title><description>We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.</description><subject>Algorithms</subject><subject>compressed sensing</subject><subject>Discrete cosine transform</subject><subject>D‐RIP</subject><subject>Fourier transforms</subject><subject>iteratively reweighted method</subject><subject>sufficient D‐NSP</subject><subject>tight frame</subject><subject>Wavelet analysis</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp10E1rwzAMBmAzNljXDfYTDLvskk624zQ-lrKPQksv29k4ttymJE3nuC3590vWXXcSSI-EeAl5ZDBhAPylrs1EgmJXZMRAqYSl0-yajIBNIUk5S2_JXdvuACBnjI_IehExmFiesOpowDOWm21ER021aUIZtzX1TaBtudmbqu2BbU4YOnruR9Q2Wwy4jzQOS9QHU-M9ufG9xIe_OiZfb6-f849kuX5fzGfLxHIlWFKgQgGG59b7XE6lBFmAA5dJW0ghvM1M7hg6j8Y6wazNFDhbcCPTvpkqMSZPl7uH0HwfsY161xzD8KTmkAuZZzyFXj1flA1N2wb0-hDK2oROM9BDXLqPSw9x9TS50HNZYfev06vV7Nf_AAEDbVg</recordid><startdate>20180930</startdate><enddate>20180930</enddate><creator>Bi, Ning</creator><creator>Liang, Kaihao</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-3000-7137</orcidid></search><sort><creationdate>20180930</creationdate><title>Iteratively reweighted algorithm for signals recovery with coherent tight frame</title><author>Bi, Ning ; Liang, Kaihao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2931-be9e30a28cff8575505b0d0d65cb533fc6a8d1edfeacd31cc690dcb2a54edf493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>compressed sensing</topic><topic>Discrete cosine transform</topic><topic>D‐RIP</topic><topic>Fourier transforms</topic><topic>iteratively reweighted method</topic><topic>sufficient D‐NSP</topic><topic>tight frame</topic><topic>Wavelet analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bi, Ning</creatorcontrib><creatorcontrib>Liang, Kaihao</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bi, Ning</au><au>Liang, Kaihao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Iteratively reweighted algorithm for signals recovery with coherent tight frame</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2018-09-30</date><risdate>2018</risdate><volume>41</volume><issue>14</issue><spage>5481</spage><epage>5492</epage><pages>5481-5492</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.5091</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-3000-7137</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0170-4214 |
| ispartof | Mathematical methods in the applied sciences, 2018-09, Vol.41 (14), p.5481-5492 |
| issn | 0170-4214 1099-1476 |
| language | eng |
| recordid | cdi_proquest_journals_2083586240 |
| source | Wiley Online Library |
| subjects | Algorithms compressed sensing Discrete cosine transform D‐RIP Fourier transforms iteratively reweighted method sufficient D‐NSP tight frame Wavelet analysis |
| title | Iteratively reweighted algorithm for signals recovery with coherent tight frame |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-12T03%3A16%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Iteratively%20reweighted%20algorithm%20for%20signals%20recovery%20with%20coherent%20tight%20frame&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Bi,%20Ning&rft.date=2018-09-30&rft.volume=41&rft.issue=14&rft.spage=5481&rft.epage=5492&rft.pages=5481-5492&rft.issn=0170-4214&rft.eissn=1099-1476&rft_id=info:doi/10.1002/mma.5091&rft_dat=%3Cproquest_cross%3E2083586240%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2083586240&rft_id=info:pmid/&rfr_iscdi=true |