Improved Analysis for SOMP Algorithm in Terms of Restricted Isometry Property

Xiaobo ZHANG  Wenbo XU  Yan TIAN  Jiaru LIN  Wenjun XU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.2   pp.533-537
Publication Date: 2020/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2055
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
compressed sensing,  SOMP algorithm,  multiple measurement vectors,  restricted isometry property,  

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Summary: 
In the context of compressed sensing (CS), simultaneous orthogonal matching pursuit (SOMP) algorithm is an important iterative greedy algorithm for multiple measurement matrix vectors sharing the same non-zero locations. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the convergence of CS algorithms. Based on the RIP of measurement matrix, this paper shows that for the K-row sparse recovery, the restricted isometry constant (RIC) is improved to $delta_{K+1}< rac{sqrt{4K+1}-1}{2K}$ for SOMP algorithm. In addition, based on this RIC, this paper obtains sufficient conditions that ensure the convergence of SOMP algorithm in noisy case.