An Improved Algorithm based on MOLS for CS

Abstract

The purpose of sparse recovery based on compressed sensing is to reconstruct sparse signals from linear compressed measurements. Greedy algorithm is often used to solve the inverse problem of underdetermined equations. Both Orthogonal Matching Pursuit(OMP) and Orthogonal Least Squares(OLS) greedy algorithms have been widely applied. Unlike the OMP algorithm, the first task of the OLS algorithm is to find the support set dropping the residual fastest. Multiple Orthogonal Least Squares(MOLS) algorithm adds the idea of multiple support set selection to the OLS algorithm, which greatly reduces the time complexity of the OLS algorithm, but needs to take the sparsity K as a priori condition. Based on this, a novel sparse recovery algorithm called Changing Stage Orthogonal Least Squares(CSOLS) is proposed in this paper. Compared with the MOLS algorithm, the most innovative feature of the CSOLS algorithm is the signal reconstruction ability without a priori information sparsity, finishing sparse recovery by conditionally broadening the search step. Compared with the MOLS algorithm and the traditional greedy algorithms with regard to the Frequency of Exact Reconstruction(FER) under the different sparsity and measurements, the CSOLS algorithm shows terrific recovery performance.