TY - GEN
T1 - Performance analysis of orthogonal matching pursuit under general perturbations
AU - Ding, Jie
AU - Chen, Laming
AU - Gu, Yuantao
PY - 2012/4/24
Y1 - 2012/4/24
N2 - As a canonical greedy algorithm, Orthogonal Matching Pursuit (OMP) is used for sparse approximation. Previous studies have mainly considered non-perturbed observations y = Φx, and focused on the exact recovery of x through y and Φ. Here, Φ is a matrix with more columns than rows, and x is a sparse signal to be recovered. This paper deals with performance of OMP under general perturbations - from both y and Φ. The main contribution shows that exact recovery of the support set of x can be guaranteed under suitable conditions. Such conditions are RIP-based, and involve the concept of sparsity, relative perturbation, and the smallest nonzero entry. In addition, certain conditions are given under which the support set of x can be reconstructed in the order of its entries' magnitude. In the end, it is pointed out that the conditions can be relaxed at the expense of a decrease in the accuracy of the recovery.
AB - As a canonical greedy algorithm, Orthogonal Matching Pursuit (OMP) is used for sparse approximation. Previous studies have mainly considered non-perturbed observations y = Φx, and focused on the exact recovery of x through y and Φ. Here, Φ is a matrix with more columns than rows, and x is a sparse signal to be recovered. This paper deals with performance of OMP under general perturbations - from both y and Φ. The main contribution shows that exact recovery of the support set of x can be guaranteed under suitable conditions. Such conditions are RIP-based, and involve the concept of sparsity, relative perturbation, and the smallest nonzero entry. In addition, certain conditions are given under which the support set of x can be reconstructed in the order of its entries' magnitude. In the end, it is pointed out that the conditions can be relaxed at the expense of a decrease in the accuracy of the recovery.
KW - Orthogonal Matching Pursuit (OMP)
KW - Restricted Isometry Property (RIP)
KW - general perturbations
KW - support recovery
UR - http://www.scopus.com/inward/record.url?scp=84859913774&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84859913774&partnerID=8YFLogxK
U2 - 10.1109/ICCNC.2012.6167553
DO - 10.1109/ICCNC.2012.6167553
M3 - Conference contribution
AN - SCOPUS:84859913774
SN - 9781467300094
T3 - 2012 International Conference on Computing, Networking and Communications, ICNC'12
SP - 892
EP - 896
BT - 2012 International Conference on Computing, Networking and Communications, ICNC'12
T2 - 2012 International Conference on Computing, Networking and Communications, ICNC'12
Y2 - 30 January 2012 through 2 February 2012
ER -