Inversion algorithm based on the generalized objective functional for compressed sensing

Owing to providing a novel insight for signal and image processing, compressed sensing (CS) has attracted increasing attention. The accuracy of the reconstruction algorithms plays an important role in real applications of the CS theory. In this paper, a generalized reconstruction model that simultaneously considers the inaccuracies on the measurement matrix and the measurement data is proposed for CS reconstruction. A generalized objective functional, which integrates the advantages of the least squares (LSs) estimation and the combinational M-estimation, is proposed. An iterative scheme that integrates the merits of the homotopy method and the artificial physics optimization (APO) algorithm is developed for solving the proposed objective functional. Numerical simulations are implemented to evaluate the feasibility and effectiveness of the proposed algorithm. For the cases simulated in this paper, the reconstruction accuracy is improved, which indicates that the proposed algorithm is successful in solving CS inverse problems.