We propose a robust and efficient algorithm for the recovery of the row-support in compressed sensing of jointly sparse signals from multiple measurement vectors (MMV). When the unknown matrix of the jointly sparse signals has full rank, MUSIC is a guaranteed algorithm for this problem, achieving the fundamental algebraic bound on the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank deficiency or bad conditioning. This situation arises with limited number of measurements, or with highly correlated signal components. In this case MUSIC fails, and in practice none of the existing MMV methods can consistently approach the algebraic bounds. The proposed algorithm, subspace-augmented MUSIC (SA-MUSIC), overcomes these limitations by combining the advantages of a greedy algorithm - a subspace version of orthogonal matching pursuit, with those of MUSIC. SA-MUSIC is a computationally efficient algorithm with good performance in both theory and practice. It is a subspace method that works with the signal subspace estimated from the MMV. The performance guarantee therefore consists of two parts. The first part bounds the noise-induced perturbation in the subspace estimation. The second part bounds the worst case and the average case performance of SA-MUSIC under this perturbation. Empirically, the recovery performance of SA-MUSIC improves on the state of the art, including that of convex relaxation algorithms, with computational cost no greater than that of greedy algorithms. 
*This work was supported in part by NSF grant No. CCF 06-35234 and NSF grant No. CCF 10-18660.