A Generalized Reconstruction Algorithm for Compressed Sensing

Abstract

Owing to providing a novel insight for the signal and image processing, compressed sensing (CS) is considered as a promising method for such fields. Successful applications of CS depend mainly on the accuracy and speed of the reconstruction algorithms. Essentially, CS reconstruction process belongs to a discrete inverse problem with finite unknown variables, methods that ensure the numerical stability while increasing the quality of a solution should be employed. In this paper, a new objective functional, which has been developed using a combinational estimation and a generalized stabilizing functional, is proposed. An efficient iterative scheme that integrates the beneficial advantages of the homotopy algorithm and the quantum particle swarm optimization (QPSO) algorithm is designed for searching a possible global optimal solution. Numerical simulations are implemented to test the validity of the proposed algorithm. Excellent numerical performances and encouraging results are observed. For the cases considered in this paper, the accuracy of the reconstructed objects is significantly improved, which indicates that the proposed algorithm is very successful in solving the CS inverse problem. As a result, a promising algorithm is introduced for CS reconstruction.