Research On Sparse Reconstruction Methods Based On The Block Structure

Compressive sensing theory has caught great attentions in the field of signal processing in recent years.This novel processing framework which combines signal acquisition and compression has been deeply investigated and widely used for reducing redundancy and waste of data.Compressive sensing requires the signal to be sparse either on its own or after some sparse transformation.In practice,many signals meet this condition and have certain inherent structures.Studies have demonstrated that for signals with non-zero elements,appearing in the form of block structures,sparse reconstruction methods exploiting the block prior information can achieve better recovery performance.Starting from the theories of compressive sensing,in this thesis firstly the sparse optimization problem and the block sparse signal model are introduced.Then the sparse Bayesian framework and the inference procedure are studies in detail.Secondly,the greedy-based reconstruction methods,including the Block Compression Sampling Matching Pursuit(Block-Co Sa MP)and Block Segmentation Orthogonal Matching Pursuit(Block-Co Sa MP),are investigated and compared by simulations.Then,the reconstruction algorithms using hypothetical prior distributions,the Clustering Sparse Bayesian Learning(Cluster-SBL)algorithm and Weighted Block Sparse Bayesian Learning(WBSBL)algorithm are studied by theoretical inference and simulations.Finally,the Total Variation Regularized Sparse Bayesian Learning(TV-SBL)reconstruction algorithm are investigated.Different from traditional block sparse recovery methods imposing regularizations on sparse signals,TV-SBL regularize the hyperparameters.In this thesis,researches are carried out on the Bayesian inference problem of TV-SBL.Simulations are performed to compare the reconstruction performance of TV-SBL with some other block sparse reconstruction methods.The experimental results show that the TV-SBL has higher reconstruction accuracy in block spare reconstruction.