  Sparse representation of a single measurement vector (SMV) has been explored
in a variety of compressive sensing applications. Recently, SMV models have
been extended to solve multiple measurement vectors (MMV) problems, where the
underlying signal is assumed to have joint sparse structures. To circumvent the
NP-hardness of the $\ell_0$ minimization problem, many deterministic MMV
algorithms solve the convex relaxed models with limited efficiency. In this
paper, we develop stochastic greedy algorithms for solving the joint sparse MMV
reconstruction problem. In particular, we propose the MMV Stochastic Iterative
Hard Thresholding (MStoIHT) and MMV Stochastic Gradient Matching Pursuit
(MStoGradMP) algorithms, and we also utilize the mini-batching technique to
further improve their performance. Convergence analysis indicates that the
proposed algorithms are able to converge faster than their SMV counterparts,
i.e., concatenated StoIHT and StoGradMP, under certain conditions. Numerical
experiments have illustrated the superior effectiveness of the proposed
algorithms over their SMV counterparts.
