TY - JOUR
T1 - The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit
AU - Liao , Anping
AU - Xie , Jiaxin
AU - Yang , Xiaobo
AU - Wang , Peng
JO - Journal of Computational Mathematics
VL - 1
SP - 70
EP - 86
PY - 2016
DA - 2016/02
SN - 34
DO - http://doi.org/10.4208/jcm.1510-m2015-0284
UR - https://global-sci.org/intro/article_detail/jcm/9783.html
KW - Compressed sensing, Sparse signal recovery, Restricted orthogonality constant
(ROC), Restricted isometry constant (RIC), Orthogonal matching pursuit (OMP).
AB - <p style="text-align: justify;">This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit (OMP) algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all $k$-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of $k$-sparse signal is also presented. Generally, the computation for the restricted isometry constant (RIC) in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all $k$-sparse signals.</p>