TY - JOUR
T1 - Recovery of sparse signals via generalized orthogonal matching pursuit
T2 - A new analysis
AU - Wang, Jian
AU - Kwon, Suhyuk
AU - Li, Ping
AU - Shim, Byonghyo
N1 - Funding Information:
The work of J. Wang and P. Li were supported in part by NSF-III-1360971, NSF-Bigdata-1419210, ONRN00014-13-1-0764, and AFOSR-FA9550-13-1-0137. The work of J. Wang was also supported in part by Grant NSFC 61532009 and Grant 15KJA520001 of Jiangsu Province. The work of B. Shim was supported in part by ICT R&D program of MSIP/IITP, B0126-15-1017, Spectrum Sensing and Future Radio Communication Platforms and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2014R1A5A1011478).
Publisher Copyright:
© 2015 IEEE.
PY - 2016/2/15
Y1 - 2016/2/15
N2 - As an extension of orthogonal matching pursuit (OMP) for improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using the restricted isometry property (RIP). We show that if a measurement matrix Φ ∈ Rm×n satisfies the RIP with isometry constant δmax{9,S+1}K ≤ 1/8, then gOMP performs stable reconstruction of all K-sparse signals x ∈ Rn from the noisy measurements y=Φ x+ v, within {K,⌊8K/S⌋ iterations, where v is the noise vector and S is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our result indicates that the number of required measurements is essentially m= O(K log n/K), which is a significant improvement over the existing result m= O(K2 log n/K), especially for large K.
AB - As an extension of orthogonal matching pursuit (OMP) for improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using the restricted isometry property (RIP). We show that if a measurement matrix Φ ∈ Rm×n satisfies the RIP with isometry constant δmax{9,S+1}K ≤ 1/8, then gOMP performs stable reconstruction of all K-sparse signals x ∈ Rn from the noisy measurements y=Φ x+ v, within {K,⌊8K/S⌋ iterations, where v is the noise vector and S is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our result indicates that the number of required measurements is essentially m= O(K log n/K), which is a significant improvement over the existing result m= O(K2 log n/K), especially for large K.
KW - Compressed Sensing (CS)
KW - Generalized Orthogonal Matching Pursuit (gOMP)
KW - Mean Square Error (MSE)
KW - Restricted Isometry Property (RIP)
KW - sparse recovery
KW - stability
UR - http://www.scopus.com/inward/record.url?scp=84961999658&partnerID=8YFLogxK
U2 - 10.1109/TSP.2015.2498132
DO - 10.1109/TSP.2015.2498132
M3 - Article
AN - SCOPUS:84961999658
SN - 1053-587X
VL - 64
SP - 1076
EP - 1089
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 4
M1 - 7321045
ER -