Nonconvex Low-rank And Convolutional Sparse Coding For MRI Reconstruction

Magnetic Resonance Imaging(MRI)has no radiation harm to human body and can image at any fault.It has become the most important technology of imaging after CT technology in the clinical diagnosis.But the slow imaging speed limits the application of MRI in more fields.In order to solve this problem,this paper proposes two methods to reconstruct magnetic resonance images: generalized nonconvex lowrank algorithm and gradient domain convolution sparse coding algorithm.(1)In the paper,we propose generalized nonconvex low-rank algorithm for MRI reconstruction,it can reconstruct the image from a k space with a low sampling rate.This algorithm is based on the theory of compressive sensing,utilizing the nonconvex function to approximate the standard 0 norm,and then use the alternative direction multiplier method to solve the calculation,so that the reconstructed image can be obtained well.(2)In this paper,we also propose a gradient domain convolution sparse coding algorithm for MRI reconstruction.In block-based feature learning algorithms,the potential structure of the signal will be broken when the image is divided into blocks.In this case,the paper solves this problem by using a global sparse distributed convolution feature.In previous studies,it has been found that the images have local similarity.Therefore,this paper maps the image into the gradient domain,and then learns filter at the horizontal and the vertical gradient image separately.Finally,we use the augmented lagrange method and the alternative direction multiplier method to solve the problem of MRI reconstruction.We have done a lot of experiments in this paper.Compared with the current algorithms,the algorithm proposed in this paper can reconstruct the texture details of the image better in the aspect of visual effect and can improve the algorithm about 2dB in terms of theoretical value.It can be seen that the proposed algorithm is more superior.