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A remark on joint sparse recovery with OMP algorithm under restricted isometry property

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  • Yang, Xiaobo
  • Liao, Anping
  • Xie, Jiaxin

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.

Suggested Citation

  • Yang, Xiaobo & Liao, Anping & Xie, Jiaxin, 2018. "A remark on joint sparse recovery with OMP algorithm under restricted isometry property," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 18-24.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:18-24
    DOI: 10.1016/j.amc.2017.07.081
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    1. Liao, Anping & Yang, Xiaobo & Xie, Jiaxin & Lei, Yuan, 2015. "Analysis of convergence for the alternating direction method applied to joint sparse recovery," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 548-557.
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