Stochastic greedy algorithms for multiple measurement vectors

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