A Fast and Noise-Robust Algorithm for Joint Sparse Recovery Through Information Transfer

In multiple measurement vector (MMV) problems, L measurement vectors each of which has length M are available for recovering jointly sparse signals that have a common support set of size K. In this paper, a fast and noise-robust greedy algorithm is proposed for joint sparse recovery in MMV problems, by exploiting a posteriori probability ratios for every index of sparse input signals. The essence of the algorithm is to transfer the information through iterations, which contributes to the performance improvement of support detection. When L is sufficiently large at M = K + 1, we investigate the asymptotic performance of exact support recovery using a Gaussian assumption, power-law approximations, and order statistics, where the techniques are inspired by experimental results. In this case, we also present a sufficient condition on the number of measurements, or M = K + 1 = Omega (log N), for theoretical support recovery guarantee. The theoretical analysis reveals that the proposed algorithm can achieve reliable joint sparse recovery asymptotically at the theoretical limit of M = K + 1 with high probability. By examining the performance for various M, K, and L, simulation results demonstrate that if M is not too small, the proposed algorithm can be reliable, fast, and noise-robust, compared to the conventional ones, such as simultaneous orthogonal matching pursuit (SOMP), subspace augmented MUSIC (SA-MUSIC), and rank-aware order recursive matching pursuit (RA-ORMP).