Recovery Conditions of Sparse Signals Using Orthogonal Least Squares-Type Algorithms

Orthogonal least squares (OLS)-type algorithms are efficient in reconstructing sparse signals, which include the well-known OLS, multiple OLS (MOLS) and block (BOLS). In this paper, we first investigate noiseless exact recovery conditions of these algorithms. Specifically, based on mutual incoherence property (MIP), provide theoretical analysis MOLS to ensure that correct nonzero support can be selected during iterative procedure. Nevertheless, for BOLS utilizes block-MIP deal with sparsity. Furthermore, MIP-based analyses extended noisy scenario. Our results indicate $K$ -sparse when MIP or SNR satisfies certain conditions, obtain reliable reconstruction at most iterations, while succeeds notation="LaTeX">$(K/d)$ iterations where notation="LaTeX">$d$ is length. It shown our derived improve existing ones, verified by simulation tests.