{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T09:13:04Z","timestamp":1773825184393,"version":"3.50.1"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"crossref","award":["12271050"],"award-info":[{"award-number":["12271050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"crossref","award":["11971491"],"award-info":[{"award-number":["11971491"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"crossref","award":["12171490"],"award-info":[{"award-number":["12171490"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Foundation of National Key Laboratory of Computational Physics","award":["6142A05230503"],"award-info":[{"award-number":["6142A05230503"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p> This paper introduces a nonconvex [Formula: see text]-analysis model: [Formula: see text] where [Formula: see text] is a measurement matrix and [Formula: see text] is a tight frame. Our main motivation is to generalize the sparse recovery via [Formula: see text] minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix [Formula: see text] such that a vector [Formula: see text] can be recovered from [Formula: see text] with a tight frame [Formula: see text] via [Formula: see text]-analysis local minimization, or any vector [Formula: see text] can be uniformly recovered from [Formula: see text] with a tight frame [Formula: see text] via [Formula: see text]-analysis minimization locally and globally. <\/jats:p>","DOI":"10.1142\/s0219691324500176","type":"journal-article","created":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T06:38:50Z","timestamp":1713508730000},"source":"Crossref","is-referenced-by-count":1,"title":["Sparse recovery with coherent frames via \u21131\u22122-analysis"],"prefix":"10.1142","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-5969-7116","authenticated-orcid":false,"given":"Xizhe","family":"Xie","sequence":"first","affiliation":[{"name":"Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6296-9947","authenticated-orcid":false,"given":"Ning","family":"Bi","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1751-0379","authenticated-orcid":false,"given":"Wengu","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China"},{"name":"National Key Laboratory of Computational Physics, Beijing 100088, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,29]]},"reference":[{"key":"S0219691324500176BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530521500068"},{"key":"S0219691324500176BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2021.09.003"},{"key":"S0219691324500176BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/060657704"},{"key":"S0219691324500176BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2288639"},{"key":"S0219691324500176BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.10.002"},{"key":"S0219691324500176BIB006","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20124"},{"key":"S0219691324500176BIB007","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.858979"},{"key":"S0219691324500176BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2007.898300"},{"key":"S0219691324500176BIB009","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/3\/035020"},{"key":"S0219691324500176BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450037906X"},{"key":"S0219691324500176BIB011","volume-title":"Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math.","author":"Daubechies I.","year":"1992"},{"key":"S0219691324500176BIB012","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"S0219691324500176BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.860430"},{"key":"S0219691324500176BIB014","doi-asserted-by":"publisher","DOI":"10.1137\/13090540X"},{"key":"S0219691324500176BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2009.10.004"},{"key":"S0219691324500176BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2008.09.001"},{"key":"S0219691324500176BIB017","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2018.2852138"},{"key":"S0219691324500176BIB018","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2014.8.761"},{"key":"S0219691324500176BIB019","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2012.2226171"},{"key":"S0219691324500176BIB020","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2191612"},{"key":"S0219691324500176BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0463-2"},{"key":"S0219691324500176BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-014-9930-1"},{"key":"S0219691324500176BIB023","doi-asserted-by":"publisher","DOI":"10.1137\/16M1098929"},{"key":"S0219691324500176BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/78.258082"},{"key":"S0219691324500176BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.04.005"},{"key":"S0219691324500176BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/s11766-022-4256-5"},{"key":"S0219691324500176BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.07.001"},{"key":"S0219691324500176BIB028","doi-asserted-by":"publisher","DOI":"10.1049\/el.2019.2205"},{"key":"S0219691324500176BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.06.003"},{"key":"S0219691324500176BIB030","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2019.2919612"},{"key":"S0219691324500176BIB031","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2262495"},{"key":"S0219691324500176BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s40305-013-0030-y"},{"key":"S0219691324500176BIB033","doi-asserted-by":"publisher","DOI":"10.1137\/15M103947X"},{"key":"S0219691324500176BIB034","doi-asserted-by":"publisher","DOI":"10.1137\/140952363"},{"key":"S0219691324500176BIB035","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-015-4234-4"},{"key":"S0219691324500176BIB036","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2705741"},{"key":"S0219691324500176BIB037","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2017.10.004"},{"key":"S0219691324500176BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/s40305-013-0013-z"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691324500176","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T04:27:54Z","timestamp":1723696074000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691324500176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,29]]},"references-count":38,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1142\/S0219691324500176"],"URL":"https:\/\/doi.org\/10.1142\/s0219691324500176","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,29]]},"article-number":"2450017"}}