On the Fundamental Limit of Orthogonal Matching Pursuit for Multiple Measurement Vector

Abstract

Given Y ∈ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m×I</sup> and A ∈ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m×n</sup> , the multiple measurement vector (MMV) problem aims to recover the support of the K-row sparse matrix X from Y = AX + E. In this paper, we present a sufficient condition for exact support recovery of K-row sparse matrices via the orthogonal matching pursuit for MMV (OMPMMV) algorithm in the noisy case. Furthermore, in the noiseless case, our proposed condition is optimal.