Generalized reconstruction algorithm for compressed sensing

Abstract

Compressed sensing (CS) is considered as a promising signal processing technique, and successful applications of the CS theory depend mainly on the accuracy and speed of the reconstruction algorithms. In this paper, a generalized objective functional, which has been developed using the combinational estimation and an extended stabilizing functional, is proposed. An efficient iterative scheme, which integrates the beneficial advantages of the homotopy method, the shuffled frog-leaping (SFL) algorithm and the harmony search (HS) algorithm, is designed for searching a possible global optimal solution. Numerical simulations are implemented to evaluate the numerical performances and effectiveness of the proposed algorithm. Excellent numerical performances and encouraging results are observed. For the cases considered in this paper, a dramatic improvement in the reconstruction accuracy is achieved, which indicates that the proposed algorithm is a promising candidate for solving CS inverse problem.