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Paper details
Number 1 - March 2020
Volume 30 - 2020
A second-order TV-based coupling model and an ADMM algorithm for MR image reconstruction
Bo Zhou, Yu-Fei Yang, Bo-Xia Hu
Abstract
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.
Keywords
MRI reconstruction, LLT model, LOT model, coupling model, ADMM, split Bregman, wavelet transform