Research And Application Of Bilinear Generalized Approximate Message Passing

Compressed Sensing(CS)is a new type of signal processing method.Its basic principle is to compress and sample data,and then use the data obtained by compression sampling to reconstruct the original signal.Bilinear Generalized Approximate Message Passing(BiGAMP)is a direct extension of Generalized Approximate Message Passing(GAMP)in compression reconstruction algorithm.It is an iterative threshold algorithm with low complexity and high performance.This dissertation focuses on the research and application of bilinear generalized message passing algorithms.Firstly,according to BiGAMP has the same bilinear character as dictionary learning,BiGAMP is proposed to be used for dictionary learning of image sparse representation.According to the property that the BiGAMP algorithm needs to conform to the Gaussian prior model,the training samples are mapped randomly to conform to the statistical model of the BiGAMP methodology.Based on this,this paper proposes a BiGAMP-based image dictionary learning method.The experimental results show that the dictionary learnt by BiGAMP has better reconstruction performance in the image CS than the dictionary learned by K-SVD.Second,according to the BiGAMP algorithm is an extension of the compression reconstruction algorithm GAMP,and the BiGAMP algorithm can be used for dictionary learning.The Blind Compressive Sensing Theory is also a compressive sensing theory based on adaptive dictionary learning.This paper designs a Blind Compressed Sensing Algorithm based on BiGAMP.It is a blind compressive sensing algorithm based on a compressible dictionary.The experimental results show that the blind compressed speech sensing algorithm based on BiGAMP performs better than the blind compression sensing based on direct method.Finally,according to the BiGAMP/EM-BiGAMP(Expectation Maximization-Bilinear Generalized Approximate Message Passing,EM-BiGAMP)algorithm,a high performance advantage can be used to solve the problem of low rank matrix filling.Low-rank matrix filling is a form of low-rank matrix recovery,and low-rank matrix recovery algorithm can be used to solve the image denoising problem.This paper proposes an image denoising algorithm based on BiGAMP/EM-BiGAMP low rank matrix recovery.Experimental results show that the image denoising algorithm based on the low rank matrix recovery of BiGAMP/EM-BiGAMP is better than other image denoising algorithms based on the low rank matrix restoration algorithm.