Abstract
Motivated by the ideas from the LOT model and its deformations, we propose a coupling model for the MR image reconstruction and apply the split Bregman iterative method on the proposed model by utilizing the augmented Lagrangian technique. The related minimization problem is then divided into four subproblems by means of the alternating minimization method. And on this basis, by combining the Barzilai-Borwein step size selection scheme, generalized shrinkage formulas, and the shrink operator, we propose an ADMM type algorithm to solve the proposed model. Several numerical examples are implemented; the experimental results demonstrate the feasibility and effectiveness of the proposed model and algorithm.
Highlights
Magnetic resonance (MR) images are obtained by placing an object in a strong magnetic field and turning on and off a radio frequency electromagnetic field
Motivated by the ideas from the LOT model and its deformations, we propose a coupling model for the MR image reconstruction and apply the split Bregman iterative method on the proposed model by utilizing the augmented Lagrangian technique
In this paper, based on the LOT model and its deformations, we proposed a coupling model for MR image reconstruction and proposed an alternating direction method of multipliers (ADMM) type algorithm to solve the proposed model
Summary
Received 1 April 2018; Revised 8 July 2018; Accepted 26 August 2018; Published 5 September 2018. Motivated by the ideas from the LOT model and its deformations, we propose a coupling model for the MR image reconstruction and apply the split Bregman iterative method on the proposed model by utilizing the augmented Lagrangian technique. The related minimization problem is divided into four subproblems by means of the alternating minimization method. On this basis, by combining the Barzilai-Borwein step size selection scheme, generalized shrinkage formulas, and the shrink operator, we propose an ADMM type algorithm to solve the proposed model. Several numerical examples are implemented; the experimental results demonstrate the feasibility and effectiveness of the proposed model and algorithm
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