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The multiple measurement vector (MMV) problem addresses the identification ofunknown input vectors that share common sparse support. Even though MMVproblems had been traditionally addressed within the context of sensor arraysignal processing, the recent trend is to apply compressive sensing (CS) due toits capability to estimate sparse support even with an insufficient number ofsnapshots, in which case classical array signal processing fails. However, CSguarantees the accurate recovery in a probabilistic manner, which often showsinferior performance in the regime where the traditional array signalprocessing approaches succeed. The apparent dichotomy between the {\emprobabilistic} CS and {\em deterministic} sensor array signal processing havenot been fully understood. The main contribution of the present article is aunified approach that unveils a {missing link} between CS and array signalprocessing. The new algorithm, which we call {\em compressive MUSIC},identifies the parts of support using CS, after which the remaining supportsare estimated using a novel generalized MUSIC criterion. Using a large systemMMV model, we show that our compressive MUSIC requires a smaller number ofsensor elements for accurate support recovery than the existing CS methods andcan approach the optimal $l_0$-bound with finite number of snapshots.

Compressive MUSIC: A Missing Link Between Compressive Sensing and Array Signal Processing