Study On SMV And MMV Problems For Sparse Signal Recovery

In this paper,we focus on the problem of sparse signal recovery,which is the fun-damental mathematical problem in Compressed Sensing.Sparse signal recovery can be interpreted as single measurement vector problem or multiple measurement problem ac-cording to the formation of the signal.Upon the convex relaxation framework of single measurement vector problem,we present an efficient algorithm for sparse signal recovery with high exact recovery prob-ability The main idea of the algorithm is to combine two existing methods:linearized Bregman algorithm and reweighting technique.We make a tradeoff between the recov-ery efficiency and the recovery ability.Compared with other available methods,such as reweighted Basis Pursuit?BP?and linearized Bregman,the proposed algorithm has a much lower computational complexity with higher probability of successful recovery.Numerical experiments demonstrate its efficiency and accuracy.On one hand,it costs half time of the reweighted BP with almost the same recovery ability,on the other hand,it can successfully recover the sparse signal with comparatively large sparsity level.Upon the l₀-minimization framework of single and multiple measurement vector problem,we introduce the heuristic computing method to this area and successfully apply the Markov Chain Monte Carlo method to solving the sparse signal recovery problem,by means of elaborate design of the target function,generation scheme of candidate solution and termination condition.We make a parallel implementation of the randomized algo-rithm which is based on MCMC,according to the natural parallelism of Markov chain.The efficiency and performance are compared among the algorithm using different num-ber of chains.The numerical experiment shows that,this algorithm can exactly recover the original signal even though the sparsity level is very high.For SMV problem,it owns much higher recovery ability than linearized Bregman and costs only half the time of S AS-R,which is the same heuristic computing type algorithm.For MMV problem,it shares almost the same recovery performance of the state-of-art M-SBL algorithm.