Multiscale reconstruction algorithm for compressed sensing

Compressed sensing (CS) method has attracted increasing attention owing to providing a novel insight for signal and image processing technology. Acquiring high-quality reconstruction results plays a crucial role in successful applications of CS method. This paper presents a multiscale reconstruction model that simultaneously considers the inaccuracy properties on the measurement data and the measurement matrix. Based on the wavelet analysis method, the original inverse problem is decomposed into a sequence of inverse problems, which are solved successively from the largest scale to the original scale. An objective functional, that integrate the beneficial advantages of the least trimmed sum of absolute deviations (LTA) estimation and the combinational M-estimation, is proposed. An iteration scheme that incorporates the advantages of the homotopy method and the evolutionary programming (EP) algorithm is designed for solving the proposed objective functional. Numerical simulations are implemented to validate the feasibility of the proposed reconstruction method.