Research On Sparse Signal Reconstruction Algorithm In Compressed Sensing

Sparse signal reconstruction is the key issue in the compressed sensing(CS),which can be applied to the single-signal and multiple-signal scenario.For the single-signal scenario,sparse signal reconstruction algorithms mainly focus on greedy algorithms,which may lead to the short-sighted and over-fitting problem.For the multi-signal scenario,the mixed support set model is the generalized model for constructing the correlation among multiple signals.Based on the mixed support set model,joint-sparse signals reconstruction algorithms do not consider how to obtain a good estimate of the common support set.Thus,they cannot meet the requirement of low sampling rate and high reconstruction precision for signals in practical applications.This article works towards overcoming the defects of greedy algorithms and improving the estimate of the common support set.The main works of this article are summarized as follows:(1)To solve the potential over-fitting problem and short-sighted problem in estimating the support set in the single-signal scenario,an optimization-oriented reconstruction algorithm is proposed in this article.The pre-selection of the support set is accomplished by greedy algorithms due to its low computational complexity.Then,a simple backtracking strategy is applied to avoid the over-fitting problem.Last,an optimization-oriented search strategy is used to sufficiently refine the support set.(2)For centralized reconstruction based on the mixed support set model in the multiple-signal scenario,the estimate of the common support set is addressed.A novel common support set refinement strategy is designed.The main idea of this strategy is roughly estimating the correct common support set and then pruning the incorrect elements with the help of overall residual error function.Based on common support set refinement,a joint-sparse signals reconstruction algorithm is proposed,where the refined common support set is used as the side information to assist in the recovery of the innovation support set.Simulation results and theoretical analysis indicate that the proposed reconstruction algorithm achieves a better estimate of the support sets and then improves the reconstruction performance for the joint-sparse signals with a moderate complexity compared with the state-of-the-art algorithms.(3)For decentralized reconstruction based on the mixed support set model in the multiple-signal scenario,the estimate of the common support set and energy consumption in transmitting and receiving messages at each sensor node is addressed.After introducing different network topologies,the common support set refinement is introduced to exactly recover the support set and further successfully reconstruct the signal at each node.Since the problem of repetitively sending and receiving messages is avoided,the energy consumption at each node is reduced.Simulation results and theoretical analysis show that the reconstruction performance improves with the increasing of network connectivity.