TY - JOUR
T1 - A Near-Optimal Restricted Isometry Condition of Multiple Orthogonal Least Squares
AU - Kim, Junhan
AU - Shim, Byonghyo
N1 - Funding Information:
This work was supported in part by the National Research Foundation of Korea (NRFK) grant funded by the Korean Government (MSIP) (2016R1A2B3015576) and in part by the Framework of International Cooperation Program managed by NRFK (2016K1A3A1A20006019).
Publisher Copyright:
© 2013 IEEE.
PY - 2019
Y1 - 2019
N2 - In this paper, we analyze the performance guarantee of multiple orthogonal least squares (MOLS) in recovering sparse signals. Specifically, we show that the MOLS algorithm ensures the accurate recovery of any K -sparse signal, provided that a sampling matrix satisfies the restricted isometry property (RIP) with \begin{equation∗} \delta -{LK-L+2} < \frac {\sqrt {L}}{\sqrt {K+2L-1}}\end{equation∗} where L is the number of indices chosen in each iteration. In particular, if L=1 , our result indicates that the conventional OLS algorithm exactly reconstructs any K -sparse vector under \delta -{K+1} < \frac {1}{\sqrt {K+1}} , which is consistent with the best existing result for OLS.
AB - In this paper, we analyze the performance guarantee of multiple orthogonal least squares (MOLS) in recovering sparse signals. Specifically, we show that the MOLS algorithm ensures the accurate recovery of any K -sparse signal, provided that a sampling matrix satisfies the restricted isometry property (RIP) with \begin{equation∗} \delta -{LK-L+2} < \frac {\sqrt {L}}{\sqrt {K+2L-1}}\end{equation∗} where L is the number of indices chosen in each iteration. In particular, if L=1 , our result indicates that the conventional OLS algorithm exactly reconstructs any K -sparse vector under \delta -{K+1} < \frac {1}{\sqrt {K+1}} , which is consistent with the best existing result for OLS.
KW - Sparse signal recovery
KW - multiple OLS (MOLS)
KW - orthogonal least squares (OLS)
KW - restricted isometry property (RIP)
UR - http://www.scopus.com/inward/record.url?scp=85065160423&partnerID=8YFLogxK
U2 - 10.1109/ACCESS.2019.2907303
DO - 10.1109/ACCESS.2019.2907303
M3 - Article
AN - SCOPUS:85065160423
SN - 2169-3536
VL - 7
SP - 46822
EP - 46830
JO - IEEE Access
JF - IEEE Access
M1 - 8674762
ER -