Bayesian stagewise week conjugate gradient pursuit algorithm for sparse signal reconstruction

A directional pursuit algorithm is proposed to reconstruct an unknown sparse signal from noisy measurements. The algorithm offered an iterative update direction for improving the reconstructive accuracy of compressive sensing. Unlike traditional directional pursuit methods which only select the atoms owning higher correlation with the residual signal, the proposed algorithm not only values the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a few are active which usually impact the reconstructive performance and decide the reconstruction dynamic range of directional pursuit methods. The others are inactive. In order to avoid redundant atoms impacting the reconstructive accuracy, Bayesian hypothesis testing model is used to identify active atoms and eliminate redundant ones. Simulation results of the proposed algorithm show that the reconstructive accuracy and reconstructive dynamic range can indeed be improved. Furthermore, better noisy immunity compared with the traditional directional pursuit methods can be obtained.