A remark on joint sparse recovery with OMP algorithm under restricted isometry property
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摘要
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.
论文关键词:Compressed sensing,Joint sparse recovery,Greedy algorithms,Orthogonal Matching Pursuit,Restricted isometry property
论文评审过程:Available online 21 September 2017, Version of Record 21 September 2017.
论文官网地址:https://doi.org/10.1016/j.amc.2017.07.081