Research On Compressed Sensing Image Reconstruction Algorithm Based On Approximate Message Passing

As an effective signal sampling method,compressed sensing breaks through the limitation of Nyquist sampling theorem,can realize the sampling and compression of sparse signal or compressible signal at the same time,and can accurately reconstruct the original signal from the undersampled measurement data.Approximate message passing(AMP)is an iterative threshold compressed sensing reconstruction algorithm with high convergence speed.In the iterative process,the denoising-based AMP algorithm uses the classical transform domain image denoising operator to achieve filtering,and achieves high image reconstruction performance.This paper is based on the theory of approximate message passing algorithm based on denoising,and the specific work is as follows:Firstly,the dictionary learning based AMP(DL-AMP)has better reconstruction performance than the AMP with fixed transform domain denoising operator.Aiming at the problem that the traditional dictionary learning requires a high number of training samples,which makes its denoising effect limited and the operation cost high in the DL-AMP iteration process,this paper designs an AMP algorithm based on clustering and sparse dictionary learning.In the iterative process,clustering is carried out according to the characteristics of image blocks,and sparse dictionaries are learned by classification to realize adaptive denoising.This algorithm reduces the requirement of dictionary learning on the number of training samples in the iterative process,and improves the quality and efficiency of image reconstruction.Secondly,an AMP algorithm based on block matching and low rank approximation is designed to solve the non-stationary characteristics of the image and the change of image noise intensity during AMP iteration.Using the noise level estimation in the iterative process,the image block size and the number of similar blocks are adaptively matched to form a low-rank matrix.Then the kernel norm minimization of Gaussian covariance matrix is used to realize the low-rank approximation of the matrix and obtain the global optimal solution,which effectively improves the denoising performance of the image.Experiments show that the algorithm has good image reconstruction performance in both quantitative and qualitative aspects.Finally,based on the effective clustering of image blocks by Gaussian mixture model,this paper designs an AMP algorithm based on Gaussian mixture model and low rank approximation.In the iterative process,Gaussian mixture model is used to cluster the image blocks,and then low-rank approximation and Wiener filtering are used to denoise the image cooperatively,which further improves the reconstruction performance of the image.In this paper,the threshold of the number of similar image blocks is set,and when the number of similar blocks is higher than the threshold,the image is restored by low-rank approximation.When the number of similar blocks is lower than the threshold,Wiener filtering is used to denoise the image.Experiments show that the algorithm can better preserve the detailed information of the image and significantly improve the reconstruction performance of the image.