  In this report, a novel efficient algorithm for recovery of jointly sparse
signals (sparse matrix) from multiple incomplete measurements has been
presented, in particular, the NESTA-based MMV optimization method. In a
nutshell, the jointly sparse recovery is obviously superior to applying
standard sparse reconstruction methods to each channel individually. Moreover
several efforts have been made to improve the NESTA-based MMV algorithm, in
particular, (1) the NESTA-based MMV algorithm for partially known support to
greatly improve the convergence rate, (2) the detection of partial (or all)
locations of unknown jointly sparse signals by using so-called MUSIC algorithm;
(3) the iterative NESTA-based algorithm by combing hard thresholding technique
to decrease the numbers of measurements. It has been shown that by using
proposed approach one can recover the unknown sparse matrix X with () Spark A
-sparsity from () Spark A measurements, predicted in Ref. [1], where the
measurement matrix denoted by A satisfies the so-called restricted isometry
property (RIP). Under a very mild condition on the sparsity of X and
characteristics of the A, the iterative hard threshold (IHT)-based MMV method
has been shown to be also a very good candidate.
