Research And Application Of Generalized Approximate Message Passing Algorithm

Compression reconstruction is an important research direction in the field of compressive sensing.Generalized Approximate Message Passing(GAMP)is a new type of compression reconstruction algorithm.Compared with other reconstruction algorithms,GAMP algorithm has the advantages of excellent phase-transition behavior,low computational complexity and so on.It is applicable to arbitrary input and output distributions and can solve nonlinear compression reconstruction problems such as phase retrieval.This paper focuses on the research of the generalized approximate message passing algorithm.The details are as follows:Firstly,in order to solve the problem of the non-convergence of the GAMP algorithm under the non-zero mean Gaussian random measurement matrix,we design a generalized orthogonal matching pursuit algorithm based on generalized approximate message passing.The algorithm finds the support through the matching pursuit algorithm at first,and then uses the GAMP algorithm to reconstruct the signal.Experiments show that the proposed algorithm effectively solves the problem of the non-convergence and enhanced robustness to non-zero-mean,column-correlated random measurement matrix.Secondly,we introduce the Cartoon-texture model in the image processing field into the framework of Compressive Phase Retrieval Algorithm via Generalized Approximate Message Passing(prGAMP).The image is decomposed into cartoon components and textures components by using two kinds of sparse representations of total variation and dual-tree complex wavelet,and we propose a phase retrieval algorithm based on cartoon texture and GAMP.Then,according to the denoisers' different performance variations with the increase of iterations,a 2-stage D-prGAMP algorithm based on cartoon-texture and BM3D(Block Matching 3D,BM3D)is proposed.Experiments show that the algorithm has better reconstructed performance with equivalent time.Finally,the adaptive damping is introduced into the phase retrieval algorithm based on cartoon-texture and GAMP and the 2-stage prGAMP algorithm respectively.The phase retrieval algorithm based on cartoon-texture and adaptive damping GAMP and 2-stage prGAMP algorithm based on adaptive damping are proposed.The experimental results show that the above algorithms significantly improve the reconstruction performance of the algorithm at the expense of a long running time.