Noise Robust Joint Sparse Recovery using Compressive Subspace Fitting

We study a multiple measurement vector (MMV) problem where m ultiple signals share a common sparse support set and are sampled by a common sensing matrix. Although we can expect that joint sparsity can improve the recovery perform ance over a single measurement vector (SMV) problem, compressive sensing (CS) algorithms for MMV exhibit performance saturation as the number of multiple signals increases. Recently, to ov erc me these drawbacks of CS approaches, hybrid algorithms that optimally combine CS wi th sensor array signal processing using a generalized MUSIC criterion have been proposed. Whi le t ese hybrid algorithms are optimal for critically sampled cases, they are not efficient in exploiting the redundant sampling to improve noise robustness. Hence, in this work, we introdu ce a novel subspace fitting criterion that extends the generalized MUSIC criterion so that it exhi bits near-optimal behaviors for various sampling conditions. In addition, the subspace fitting crit erion leads to two alternative forms of compressive subspace fitting (CSF) algorithms with forward n backward support selection, which significantly improve the noise robustness. Numerica l simulations show that the proposed algorithms can nearly achieve the optimum.