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

作者：Yang, Xiaobo; Liao, Anping^*; Xie, Jiaxin

来源：Applied Mathematics and Computation, 2018, 316: 18-24.

DOI：10.1016/j.amc.2017.07.081

• Compressed sensing
• Joint sparse recovery
• Greedy algorithms
• Orthogonal Matching Pursuit
• Restricted isometry property

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 delta(K+1) of the measurement matrix A satisfies delta(K+1) < 1/(root K+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 delta(K+1) = 1/(root K+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 delta(K+1) = 1/root K by Mo and Shen [12] which can not guarantee OMP to exactly recover some K-sparse signals.

• 出版日期2018-1-1
• 单位湖南大学