Recovery Analysis Of Block-sparse Signal Via（truncated）?₂/?₁ Minimization With Redundant Dictionaries

With the the application of Big Data to various fields,it has been becoming increasingly indispensable to people’s life.Nowadays,as data are more complex and changing and of high value,how to deal with these data effectively has been a focus of academic study.The compressed sensing theory has been proved efficient and effective in processing these high-dimensional data.It first employs proper dictionary to represent the sparsity of signal,and then recovers accurately the original signal by means of dimensionality reduction and recovery algorithm.this theory has found wide application in the fields of medical imaging,wireless communications,image processing,pattern recognition,information theory,etc.This paper,based on the theory of compressed sensing,studies the recovery of the block sparse signal with redundant dictionaries.The main contents of this thesis are as follows:Chapter 1 gives an introduction to the background of compressed sensing theory and its advantages over the traditional sampling methods,an overview of the researches in compressed sensing and block compressed sensing theory with redundant dictionaries,and the general structure of this paper.Chapter 2 presents the traditional researches in compressed sensing with redundant dic-tionaries,and the related contents of block compressed sensing theory with redundant dictio-naries for block structure data.Chapter 3,based on the theory of block compressed sensing,proposes a truncated ?₂/?₁-minimization model with redundant dictionaries,discusses how to use the condition of re-stricted orthogonality property and restricted isometry property to get the error of the model when the block-restricted isometry constant δ_k+[t/2]|τ at （0,0.307）.Based on the discrete cosine transform dictionary,the algorithm is proved effective for signal recovery using the alternating direction method of multipliers algorithm.Chapter 4 first introduces the data separation model for multi-modal data,and then studies the ?₂/?₁ compressed data separation model under complete perturbation with the redundant dictionaries thanks to block compressed sensing theory.The perturbed block constrained condition with the redundant dictionaries is used to obtain the error upper limit of the model.Finally,the algorithm is proved effective using the block iterative weighted least squares algorithm.Chapter 5 summarizes the main findings of the paper,and gives suggestions on the further researches in the truncated block compressed sensing and compressed block data separation with redundant dictionaries.