期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2020
卷号：30
期号：1
页码：113-122
DOI：10.34768/amcs-2020-0009
出版社：De Gruyter Open
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.
