Machine Learning Algorithm Based On The Frame-work Of Message Passing

This thesis mainly studies the signal recovery algorithms in the field of compressed sensing(CS),which can be divided into three categories: hand-designed methods,data-driven method and model-driven method.The hand-designed method depends on the prior information of the target signal,which is usually understandable.Such as approximate message passing(AMP)and generalized approximate message passing(GAMP),etc.The data-driven method uses neural network to learn the structure of data and the prior information of target signal,but there is almost no theory to support the performance of the method and only suitable for specific settings.The model-driven method takes into account both the hand-designed method and the data-driven method.For example,the learned D-AMP(LD-AMP)combines the denoising-based AMP(D-AMP)and the denoising convolutional neural network(Dn CNN).However,LD amp model can't deal with the signal reconstruction of generalized linear model(GLM).In this paper,a generalized approximate message passing algorithm based on denoising(D-GAMP)is proposed to expand GAMP algorithm,so that the D-GAMP algorithm no longer depends on the prior distribution of the target signal.In the D-GAMP algorithm,the denoisier is combined with GAMP algorithm,and the denoisier adopts high-performance image denoising algorithm,such as block matching and 3-D filtering(BM3D),etc.Then in order to improve the performance of D-GAMP algorithm,this paper proposes a learning based generalized approximate message passing algorithm(LD-GAMP).The LD-GAMP model adopts the idea of "unrolling" into D-GAMP,which expands the D-GAMP algorithm into a series of D-GAMP layers(iterations)to form a network framework.In each D-GAMP layer,there is a denoising convolution neural network based on the residual neural network(Res Net).LD-GAMP model not only has higher applicability,but also has lower complexity.Firstly,compared with LD-AMP model and GAMP algorithm,LD-GAMP model can reconstruct the target signal with high performance from the quantitative observation data;secondly,the number of parameters is only half of LD-AMP model(based on Dn CNN).Therefore,LD-GAMP model is more stable and easier to train.In addition,because the LD-GAMP model is based on GAMP algorithm,it is not sensitive to the change of measurement matrix,compression ratio and noise level.