TY - JOUR
T1 - Required Number of Iterations for Sparse Signal Recovery via Orthogonal Least Squares
AU - Li , Haifeng
AU - Zhang , Jing
AU - Wen , Jinming
AU - Li , Dongfang
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 17
PY - 2022
DA - 2022/11
SN - 41
DO - http://doi.org/10.4208/jcm.2104-m2020-0093
UR - https://global-sci.org/intro/article_detail/jcm/21167.html
KW - Sparse signal recovery, Orthogonal least squares (OLS), Restricted isometry property (RIP).
AB - <p style="text-align: justify;">In countless applications, we need to reconstruct&nbsp; a $K$-sparse signal $\mathbf{x}\in\mathbb{R}^n$ from noisy measurements $\mathbf{y}=\mathbf{\Phi}\mathbf{x}+\mathbf{v}$,&nbsp; 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,&nbsp; 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 $\mathbf{x}$&nbsp; 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.</p>