{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:54:10Z","timestamp":1759042450865,"version":"3.37.3"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61411146001"],"award-info":[{"award-number":["61411146001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>This paper first presents a new generally perturbed compressed sensing (CS) model<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>y<\/mml:mi><mml:mo>=<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>A<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>E<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>+<\/mml:mo><mml:mi>e<\/mml:mi><\/mml:math>, which incorporated a general nonzero perturbation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><\/mml:math>into sensing matrix<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math>and a noise<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math>into signal<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:math>simultaneously based on the standard CS model<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>y<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>A<\/mml:mi><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>e<\/mml:mi><\/mml:math>and is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi mathvariant=\"normal\">R<\/mml:mi><mml:mi mathvariant=\"normal\">I<\/mml:mi><mml:mi mathvariant=\"normal\">P<\/mml:mi><\/mml:math>) and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noise<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>e<\/mml:mi><\/mml:mrow><\/mml:math>, signal noise<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math>, and perturbation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><\/mml:math>involved.<\/jats:p>","DOI":"10.1155\/2016\/5094239","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T19:43:56Z","timestamp":1459367036000},"page":"1-13","source":"Crossref","is-referenced-by-count":1,"title":["Noise Folding in Completely Perturbed Compressed Sensing"],"prefix":"10.1155","volume":"2016","author":[{"given":"Limin","family":"Zhou","sequence":"first","affiliation":[{"name":"Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Xinxin","family":"Niu","sequence":"additional","affiliation":[{"name":"Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Jing","family":"Yuan","sequence":"additional","affiliation":[{"name":"Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]}],"member":"311","reference":[{"key":"13","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2005.862083"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2006.871582"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1109\/msp.2007.914729"},{"key":"12","first-page":"1","volume-title":"Introduction to compressed sensing","volume":"93","year":"2011"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4948-7"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2004.831016"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2009.2025154"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2010.2054730"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2007.909108"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2010.2054653"},{"issue":"3","key":"23","volume":"27","year":"2011","journal-title":"Inverse Problems"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2011.2176936"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2012.2185923"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2008.07.002"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2012.2196256"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2010.2042412"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2005.860430"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20124"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2005.858979"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/lsp.2011.2159837"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/jstsp.2009.2039170"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2012.2222377"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/5094239.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/5094239.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/5094239.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T12:53:42Z","timestamp":1469537622000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2016\/5094239\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":22,"alternative-id":["5094239","5094239"],"URL":"https:\/\/doi.org\/10.1155\/2016\/5094239","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2016]]}}}