Reconstruction Of Block Sparse Signals Based On ?1-2 Minimization Method

In recent years,with the continuous advancement of national science and technology,information has become an indispensable factor in the development of all walks of life,and the acquisition of relevant data through a large amount of information has gradually become an indispensable trend.How to effectively mine and Dealing with these data has always been a hot topic in the academic world.In recent years,the theory of compressed sensing proposed by Donoho et al.has brought a breakthrough in processing these data,which integrates data collection and compression,with less The observations are used to reconstruct the original signal,which greatly improves the efficiency of the reconstructed signal.This paper studies the theory of block compression sensing based on the theory of compressed sensing,making full use of the?_1-2minimization method and discussing its The case of recovering block sparse vectors under truncated conditions and non-Gaussian conditions,the main contents are as follows:The first chapter introduces the research background,research status and progress of the theory of compressed sensing,and further introduces the?_1-2minimization method and its promotion.The second chapter introduces the traditional knowledge of compressed sensing and block compression sensing,and leads to the model of recovering block sparse vector by?_1-2min-imization method.Then the truncation needed for the research content of this paper The conditional and non-Gaussian conditions are introduced,and the model under the correspond-ing conditions is proposed.The third chapter introduces the block sparse compressed sensing based on the mini-mization of the?_1-2method under truncation conditions.The truncation of the algorithm of the previous block?_1-2is added.And the theoretical analysis related to this algorithm is established,including the reconstruction conditions of the algorithm and the upper bound of the error.Especially in the theoretical analysis,the proposed reconstruction conditions are better than the existing ones.Subsequent numerical experiments are also The effectiveness of the block sparse vector algorithm using the?_1-2method under truncation conditions is verified.The fourth chapter uses the?_1-2minimization method to recover block sparse vectors under non-Gaussian noise conditions.In addition to the relevant theoretical analysis,in the paper,make full use of the advantages of ADMM algorithm.To ensure the accurate reconstruction of the block sparse signal under non-Gaussian noise conditions.Experiments show that the performance of the proposed algorithm in different situations has a greater advantage than other models.In the fifth chapter,the thesis is summarized,and the research on block compression perception under the?_1-2minimization method is analyzed and forecasted.