The analysis of completely perturbed model based on RIP via orthogonal least squares.

Orthogonal least squares (OLS) algorithm, as a popular greedy algorithm for sparse signal recovery, has attracted much attention in recent years. In this paper, the completely perturbed model is considered, y∼=Ax+b,A∼=A+E, $\tilde{\mathbf{y}}=\mathbf{A}\mathbf{x}+\mathbf{b},\tilde{\mathbf{A}}=\mathbf{A}+\mathbf{E},$ where x is K‐sparse. Assume that the matrix A∼ $\tilde{\mathbf{A}}$ has unit ℓ2‐norm columns and satisfies the restricted isometry property of order K + 1. Given stopping criterion ‖r∼k‖≤ε0 ${\Vert}{\tilde{\mathbf{r}}}^{k}{\Vert}\le {\varepsilon }_{0}$, then the authors prove that the OLS algorithm precisely recovers the support of the K‐sparse signal x in at most K iterations under the suitable constraint condition on x. In addition, the authors also show that the authors' conclusion is superior to the current results. [ABSTRACT FROM AUTHOR]