Research on Split Augmented Largrangian Shrinkage Algorithm in Magnetic Resonance Imaging Based on Compressed Sensing

This paper aims to meet the requirements of reducing the scanning time of magnetic resonance imaging(MRI), accelerating MRI and reconstructing a high quality image from less acquisition data as much as possible. MRI method based on compressed sensing(CS) with multiple regularizations(two regularizations including total variation(TV) norm and L1 norm or three regularizations consisting of total variation, L1 norm and wavelet tree structure) is proposed in this paper, which is implemented by applying split augmented lagrangian shrinkage algorithm(SALSA). To solve magnetic resonance image reconstruction problems with linear combinations of total variation and L1 norm, we utilized composite split denoising(CSD) to split the original complex problem into TV norm and L1 norm regularization subproblems which were simple and easy to be solved respectively in this paper. The reconstructed image was obtained from the weighted average of solutions from two subproblems in an iterative framework. Because each of the splitted subproblems can be regarded as MRI model based on CS with single regularization, and for solving the kind of model, split augmented lagrange algorithm has advantage over existing fast algorithm such as fast iterative shrinkage thresholding(FIST)and two step iterative shrinkage thresholding(Tw IST) in convergence speed. Therefore,we proposed to adopt SALSA to solve the subproblems. Moreover, in order to solve magnetic resonance image reconstruction problems with linear combinations of total variation, L1 norm and wavelet tree structure, we can split the original problem into three subproblems in the same manner, which can be processed by existing iteration scheme.A great deal of experimental results show that the proposed methods can effectively reconstruct the original image. Compared with existing algorithms such as TVCMRI,Rec PF, CSA, FCSA and Wa TMRI, the proposed methods have greatly improved the quality of the reconstructed images and have better visual effect.