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.

中文翻译：

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多个测量向量的随机贪婪算法

在各种压缩感测应用中已经探索了单个测量向量（SMV）的稀疏表示。最近，SMV模型已扩展为解决多个测量向量（MMV）问题，其中假定基础信号具有联合稀疏结构。为了规避\ ell_0 $最小化问题的NP难度，许多确定性MMV算法以有限的效率求解凸松弛模型。在本文中，我们开发了用于解决联合稀疏MMV重建问题的随机贪婪算法。特别是，我们提出了MMV随机迭代硬阈值（MStoIHT）和MMV随机梯度匹配追踪（MStoGradMP）算法，并且我们还利用了迷你批处理技术来进一步提高其性能。收敛性分析表明，在某些条件下，所提出的算法能够比其SMV对应算法（即串联的StoIHT和StoGradMP）收敛更快。数值实验表明，所提出的算法优于SMV对应算法。