(untitled) (Journal of Computational Mathematics, 2022)
In countless applications, we need to reconstruct a K-sparse signal xR^n from noisy measurements y=Φx+v, where ΦR^m× n is a sensing matrix and vR^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 x with the OLS algorithm. We show that OLS provides a stable reconstruction of all K-sparse signals x in 2.8K ceil iterations provided that Φ 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.