A Second–Order TV–Based Coupling Model and an ADMM Algorithm for MR Image Reconstruction

International Journal of Applied Mathematics and Computer Science

Zhou Bo¹  Hu Bo-Xia¹  Yang Yu-Fei² 

[1] College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China;School of Computer Engineering and Applied Mathematics, Changsha University, Changsha 410003, Hunan, China;

关键词: mri reconstruction;    llt model;    lot model;    coupling model;    admm;    split bregman;    wavelet transform;   

DOI  :  10.34768/amcs-2020-0009

来源: DOAJ

【 摘 要 】

Motivated by ideas from two-step models and combining second-order TV regularization in the LLT model, we propose a coupling model for MR image reconstruction. By applying the variables splitting technique, the split Bregman iterative scheme, and the alternating minimization method twice, we can divide the proposed model into several subproblems only related to second-order PDEs so as to avoid solving a fourth-order PDE. The solution of every subproblem is based on generalized shrinkage formulas, the shrink operator or the diagonalization technique of the Fourier transform, and hence can be obtained very easily. By means of the Barzilai–Borwein step size selection scheme, an ADMM type algorithm is proposed to solve the equations underlying the proposed model. The results of numerical implementation demonstrate the feasibility and effectiveness of the proposed model and algorithm.

【 授权许可】

Unknown