Year: 2023
Author: Haifeng Li, Jing Zhang, Jinming Wen, Dongfang Li
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 1–17
Abstract
In countless applications, we need to reconstruct a $K$-sparse signal $\mathbf{x}\in\mathbb{R}^n$ from noisy measurements $\mathbf{y}=\mathbf{\Phi}\mathbf{x}+\mathbf{v}$, where $\mathbf{\Phi}\in\mathbb{R}^{m\times n}$ is a sensing matrix and $\mathbf{v}\in\mathbb{R}^m$ is a noise vector. Orthogonal least squares (OLS), which selects at each step the column that results in the most significant decrease in the residual power, is one of the most popular sparse recovery algorithms. In this paper, we investigate the number of iterations required for recovering $\mathbf{x}$ with the OLS algorithm. We show that OLS provides a stable reconstruction of all $K$-sparse signals $\mathbf{x}$ in $\lceil2.8K\rceil$ iterations provided that $\mathbf{\Phi}$ satisfies the restricted isometry property (RIP). Our result provides a better recovery bound and fewer number of required iterations than those proposed by Foucart in 2013.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2104-m2020-0093
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 1–17
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Sparse signal recovery Orthogonal least squares (OLS) Restricted isometry property (RIP).