  The multiple measurement vector (MMV) problem addresses the identification of
unknown input vectors that share common sparse support. Even though MMV
problems had been traditionally addressed within the context of sensor array
signal processing, the recent trend is to apply compressive sensing (CS) due to
its capability to estimate sparse support even with an insufficient number of
snapshots, in which case classical array signal processing fails. However, CS
guarantees the accurate recovery in a probabilistic manner, which often shows
inferior performance in the regime where the traditional array signal
processing approaches succeed. The apparent dichotomy between the {\em
probabilistic} CS and {\em deterministic} sensor array signal processing have
not been fully understood. The main contribution of the present article is a
unified approach that unveils a {missing link} between CS and array signal
processing. The new algorithm, which we call {\em compressive MUSIC},
identifies the parts of support using CS, after which the remaining supports
are estimated using a novel generalized MUSIC criterion. Using a large system
MMV model, we show that our compressive MUSIC requires a smaller number of
sensor elements for accurate support recovery than the existing CS methods and
can approach the optimal $l_0$-bound with finite number of snapshots.
