Year: 2015
Author: Zhiqiang Xu
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 495–516
Abstract
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 $M$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1505-m4529
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 495–516
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Sparse signals Compressed sensing Greedy algorithms