Image Compressive Sensing Reconstruction Based On Approximate Message Passing With Low Rank Denoising

As a new signal sampling theory,compressive sensing theory indicates that for the sparse or compressible signal,we can accurately reconstruct the measured data far below the Shannon sampling rate.Once the compressive sensing theory was proposed,it has been attracted widely attention by academia and industry.It has shown good application prospects in signal processing,pattern recognition,communication,optical/microwave imaging and other fields.Designing the reconstruction algorithm to recover the original signal from a small number of measurements,which is one of the cores of the compressive sensing theory.Traditional natural image compressive sensing reconstruction based on sparse constraint mainly faces two problems.One is that the non-stationary of natural image makes it difficult to find its perfect sparse representation.The other is that the sampling data scale of natural image is usually large.The former limits the reconstruction efficiency of the reconstruction algorithm,while the latter makes the computational complexity of the reconstruction algorithm too high.Therefore,this paper focuses on the research of image compressive sensing reconstruction based on image non-local sparse theory and approximate message passing framework,in order to achieve fast reconstruction of large scale image signal,and improve the efficiency of reconstruction effectively.The main work and contribution of this paper are as follows:(1)Research on an image compressive sensing reconstruction method based on approximate message passing with adaptive low rank denoising.The non-local low rank priori feature implied in images has been successfully used in image restoration applications such as denoising.Aiming at the non-stationary characteristic of natural images and the variation of images noise intensity in iterative reconstruction,an adaptive low rank denoising approximate message passing image compressive sensing recovery method is constructed.Specifically,according to the noise variance estimation of the iterative reconstructed image,the size of the block images and the size of similar blocks are adaptively adjusted to improve the performance of low-rank denoising effectively,thus ensuring the convergence speed of the iterative reconstructed image and improving the quality of the reconstructed image.A large number of experimental results show that the method has good reconstruction performance in noiseless and noisy observation environment,and can effectively preserve the texture details of the images.(2)Research on an image compressive sensing reconstruction method based on approximate message passing with Gaussian mixture models and low-rank denoising.In order to find similar image blocks constructing non-local low rank matrices,Euclidean distance-based similarity measurement method is usually used,but this method does not take into account the structural statistical similarity between image blocks.To solve this problem,an image similarity block extraction method based on Gaussian mixture models is proposed.Specifically,the statistical probability distribution of different Gaussian components in natural images blocks are firstly learned by using the Gaussian mixture models,and then the more real and similar image blocks are found more accurately according to the best representation of a certain Gaussian component in the learning models during the extraction of similar image blocks.By using the similar block extraction method based on Gaussian mixture models,the good low rank feature of non-local similar block groups are more effectively guaranteed.Finally,the low rank denoising of similar block groups is accomplished by adaptive weighted singular value soft threshold filtering,which effectively preserves the details of the images.The effectiveness of the proposed method is verified by comparing the performance of the proposed method with that of other similar algorithms.