 A remark on joint sparse recovery with OMP algorithm under restricted isometry propertyXiaobo Yang, Anping Liao and Jiaxin Xie Applied Mathematics and Computation, 2018, vol. 316, issue C, 18-24 Abstract: The theory and algorithms for recovering a sparse representation of multiple measurement vector (MMV) are studied in compressed sensing community. The sparse representation of MMV aims to find the K-row sparse matrix X such that Y=AX, where A is a known measurement matrix. In this paper, we show that, if the restricted isometry property (RIP) constant δK+1 of the measurement matrix A satisfies δK+1<1K+1, then all K-row sparse matrices can be recovered exactly via the Orthogonal Matching Pursuit (OMP) algorithm in K iterations based on Y=AX. Moreover, a matrix with RIP constant δK+1=1K+0.086 is constructed such that the OMP algorithm fails to recover some K-row sparse matrix X in K iterations. Similar results also hold for K-sparse signals recovery. In addition, our main result further improves the proposed bound δK+1=1K by Mo and Shen [12] which can not guarantee OMP to exactly recover some K-sparse signals. Keywords: Compressed sensing; Joint sparse recovery; Greedy algorithms; Orthogonal Matching Pursuit; Restricted isometry property (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:316:y:2018:i:c:p:18-24 DOI: 10.1016/j.amc.2017.07.081 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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