Variable Step Size Adaptive Forward-Backward Pursuit Algorithm

• 1、School of Information and Communications, Universtiy of Posts and Telecommunications, Chongqing 400065
• 2、School of Information and Communications, University of Posts and Telecommunications, Chongqing 400065

Abstract：Aiming at the problem that Forward-Backward Pursuit (FBP) alogrithm cannot change its step sizes and make the algorithm a low accuracy in reconstuction, in order to improve the recovery performance of FBP algorithm, Variable Step Size Adaptive Forward-Backward Pursuit (VsAFBP) algorithm was proposed in this paper. Firstly, before each iteration, VsAFBP did pseudo-inverse processing on observation matrix, which could reduce the coherence between the atoms, thereby improveing the accuracy of the selected atoms. Secondly, in each iteration, the proposed algorithm pruned atoms adaptively by comparing the size of residual before and after atom prunning. Finally, VsAFBP incorporated a variable step size strategy. In the early stage of iteration, a large step sizes were used to reduce the iterative times, and then the step sizes were replaced by small ones to imprve the reconstruction precision. The experimental results show that the proposed algorithm perfoms better than FBP algorithm for both one-dimensional Gaussian random signal and two-dimensional image signal.

Keywords： compressed sensing greedy algorithm sparse signal Forward-Backward Pursuit.