TY - GEN
T1 - Compressive MUSIC with optimized partial support for joint sparse recovery
AU - Kim, Jong Min
AU - Lee, Ok Kyun
AU - Ye, Jong Chul
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80054808061&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2011.6034213
DO - 10.1109/ISIT.2011.6034213
M3 - Conference contribution
AN - SCOPUS:80054808061
SN - 9781457705953
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 658
EP - 662
BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Y2 - 31 July 2011 through 5 August 2011
ER -