Compressive MUSIC with optimized partial support for joint sparse recovery

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. The MMV problem has been traditionally addressed either by sensor array signal processing or compressive sensing. However, recent breakthroughs in this area such as compressive MUSIC (CS-MUSIC) or subspace-augumented MUSIC (SA-MUSIC) optimally combine the compressive sensing (CS) and array signal processing such that k - r supports are first found by CS and the remaining r supports are determined by a generalized MUSIC criterion, where k and r denote the sparsity and the number of independent snapshots, respectively. Even though such a hybrid approach significantly outperforms the conventional algorithms, its performance heavily depends on the correct identification of k-r partial support by the compressive sensing step, which often deteriorates the overall performance. The main contribution of this paper is, therefore, to show that as long as k - r + 1 correct supports are included in any k-sparse CS solution, the optimal k - r partial support can be found using a subspace fitting criterion, significantly improving the overall performance of CS-MUSIC. Furthermore, unlike the single measurement CS counterpart that requires infinite SNR for a perfect support recovery, we can derive an information theoretic sufficient condition for the perfect recovery using CS-MUSIC under a finite SNR scenario.