Noise Robust Joint Sparse Recovery using Compressive Subspace Fitting

We study a multiple measurement vector (MMV) problem where multiple 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 performance 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 overcome these drawbacks of CS approaches, hybrid algorithms that optimally combine CS with sensor array signal processing using a generalized MUSIC criterion have been proposed. While these 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 introduce a novel subspace fitting criterion that extends the generalized MUSIC criterion so that it exhibits near-optimal behaviors for various sampling conditions. In addition, the subspace fitting criterion leads to two alternative forms of compressive subspace fitting (CSF) algorithms with forward and backward support selection, which significantly improve the noise robustness. Numerical simulations show that the proposed algorithms can nearly achieve the optimum.