Application Research On Split Augmented Largrangian Shrinkage Algorithm In MRI Based On Compressed Sensing

In order to meet the demand of reducing scan 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 Norm and L1Norm or three regularizations consist of total variation, L1norm and Wavelet tree structure) is proposed in this paper, which is implemented by applying Split Augmented Lagrangian Shrinkage Algorithm (SALSA). Since the MRI model based on multiple regularizations fully considers the priori information of images, and further constrains the objective function, so the model can more accurately reconstruct the original images. However, it is not only very difficult to solve directly but also has a great amount of computation. To solve Magnetic Resonance image reconstruction problems with linear combinations of Total Variation and L1norm, we utilize Composite Split Denoising (CSD) to split the original complex problem into TV norm and L1norm regularization subproblems which are simple and easy to be solved respectively in this paper. The reconstructed image is 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 FIST and TwIST in convergence speed. Therefore, we propose to adopt SALSA to solve the subproblems. Moreover, in order to solve Magnetic Resonance image reconstruction problems with linear combinations of Total Variation, L1norm 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 shows that the proposed methods can effectively reconstruct the original image. Compared with existing algorithms such as TVCMRI, RecPF, CSA, FCSA and WaTMRI, the proposed methods have greatly improved the quality of the reconstructed image and have better visual effects.