<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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....

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

Published Online: Apr 03, 2020

Page range: 113 - 122

Received: Oct 18, 2018

Accepted: Jul 08, 2019

DOI: https://doi.org/10.34768/amcs-2020-0009

Keywords
MRI reconstruction, LLT model, LOT model, coupling model, ADMM, split Bregman, wavelet transform

© 2020 Bo Zhou et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Apr 03, 2020

Page range: 113 - 122

Received: Oct 18, 2018

Accepted: Jul 08, 2019

DOI: https://doi.org/10.34768/amcs-2020-0009

KeywordsMRI reconstruction, LLT model, LOT model, coupling model, ADMM, split Bregman, wavelet transform

© 2020 Bo Zhou et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
MRI reconstruction, LLT model, LOT model, coupling model, ADMM, split Bregman, wavelet transform