TY - JOUR
T1 - The Performance of Orthogonal Multi-Matching Pursuit under the Restricted Isometry Property
AU - Xu , Zhiqiang
JO - Journal of Computational Mathematics
VL - 5
SP - 495
EP - 516
PY - 2015
DA - 2015/10
SN - 33
DO - http://doi.org/10.4208/jcm.1505-m4529
UR - https://global-sci.org/intro/article_detail/jcm/9856.html
KW - Sparse signals, Compressed sensing, Greedy algorithms
AB - <p style="text-align: justify;">The orthogonal multi-matching pursuit (OMMP) is a natural extension of the orthogonal matching pursuit (OMP).We denote the OMMP with the parameter $M$ as OMMP($M$) where $M$ ≥ 1 is an integer. The main difference between OMP and OMMP($M$) is that OMMP($M$) selects $M$ atoms per iteration, while OMP only adds one atom to the optimal atom set. In this paper, we study the performance of orthogonal multi-matching pursuit under RIP. In particular, we show that, when the measurement matrix $A$ satisfies (25$s$, 1/10)-RIP, OMMP($M_0$) with $M_0$ = 12 can recover $s$-sparse signals within $s$ iterations. We furthermore prove that OMMP($M$) can recover $s$-sparse signals within $O(s/M)$ iterations for a large class of $M$.</p>