Application Research Of Bilinear Adaptive Vector Approximation Message Passing

The basic principle of compressed sensing theory is to compress and sample the signal,and then reconstruct the original signal using the data obtained from compressed sampling.The Vector Approximate Message Passing(VAMP)algorithm is a compression and reconstruction algorithm with the advantages of low computational complexity and high reconstruction accuracy.When the algorithm is applied to compressed sensing reconstruction,the measurement matrix can use a random matrix with right orthogonal invariance.The Bilinear Adaptive Vector Approximation Message Passing(BADVAMP)algorithm is an extension of the compression reconstruction algorithm VAMP.This article mainly focuses on the research and application of BADVAMP algorithm in the following aspects:Firstly,a dictionary learning algorithm based on BADVAMP is studied.Based on the bilinear property of BADVAMP algorithm,the algorithm is applied to the direction of dictionary learning.The dictionary learning algorithm based on BADVAMP solves the problem that Bilinear Generalized Message Passing(Bi GAMP)based on Approximate Message Passing is only suitable for Gaussian priori.It expands the scope of application of BADVAMP dictionary learning.Meanwhile,this paper studies the dictionary learning algorithm based on Bilinear Adaptive Generalized Vector Approximate Message Passing(BADGVAMP).BADGVAMP algorithm is an extension of BADVAMP algorithm.Experimental results show that compared with Bi GAMP and K-SVD algorithm,the dictionary based on BADVAMP and BADGVAMP algorithm achieves superior image reconstruction quality when applied to compressed sensingSecondly,using blind compressed sensing theory,an algorithm based on Bilinear Adaptive Vector Approximate Message Passing-Blind Compressed Sensing(BADVAMP-BCS)is designed.This algorithm can recover the original signal from a few measured signals when the sparse basis is unknown.The experimental results show that,compared with the blind compressed sensing algorithm of direct method and the blind compressed sensing algorithm based on Bi GAMP,BADVAMP-BCS algorithm can reconstruct image details more clearly,and has more diversity in the selection of observation matrix.