Improved Analysis for SOMP Algorithm in Terms of Restricted Isometry Property

抄録

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 $\delta_{K+1}<\frac{\sqrt{4K+1}-1}{2K}$ for SOMP algorithm. In addition, based on this RIC, this paper obtains sufficient conditions that ensure the convergence of SOMP algorithm in noisy case.