Maximal-minimal correlation atoms algorithm for sparse recovery

Abstract

A new iterative algorithm is proposed to reconstruct an unknown sparse signal from a set ol projected measurements. Unl ike existing greedy pursuit methods which only consider the atoms having the highest correlation with the residual signal, the prop osed algorithm not only considers the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a tew are correct which usually impact the reconstructive performance and decide the rec onstruction dynamic range of greedy pursuit methods. The others are redundant. In order to avoid redundant atoms impacting the reconstructive accuracy, the Bayesian pursuit algorithm is used to eliminate them. Simulation results show that the proposed alg orithm can improve the reconstructive dynamic range and the reconstructive accuracy. Furthermore, better noise immunity comp ared with the existing greedy pursuit methods can be obtained.