The Multiple Measurement Vectors (MMV) problem addresses the recovery of unknown input vectors which share the same sparse support. The Compressed Sensing (CS) has the capability of estimating the sparse support even in coherent cases, where the traditional array processing approaches like MUltiple SIgnal Classification (MUSIC) often fail. However, CS guarantees the accurate recovery in a probabilistic manner, and often shows inferior performance in cases where the traditional ways succeed. Recently, a novel compressive MUSIC (or CS-MUSIC) algorithm is proposed by Kim et al., in which both the advantages of CS and traditional MUSIC-like methods are combined together. As an iterative projecting algorithm, Difference Map (DM) is first used to solve the phase retrieval problem in crystallography. Recent results show that it has excellent performance in solving a wide variety of non-convex problems like compressed sensing. In this paper, a DM-based CS-MUSIC algorithm is proposed. Experiments show that the proposed algorithm is very effective in MMV problem solving and the success rate of CS-MUSIC is dramatically improved.
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