Performance of orthogonal matching pursuit for multiple measurement vectors with noise

Abstract

Orthogonal matching pursuit (OMP) algorithm for the multiple measurement vectors (MMV) is a greedy method to find the sparse matrix with few nonzero rows that represents the measurement vectors under the sensing matrix. This paper analyzes the recovery performance of OMP for MMV (OMPMMV) in the bounded noise scenarios, and provides the sufficient conditions that are related to the sensing matrix and sparse matrix for exact support recovery. We start with the intuitive sufficient conditions for exact support recovery, and then apply these conditions to scenarios of two types of bounded noise. The results show that under some conditions on the coherence of the sensing matrix and the minimum l2 norm of any nonzero row vector from the sparse matrix, exact support recovery of sparse matrix can be guaranteed.