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 -

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.