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Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers

Part of: Numerical methods in calculus of variations and optimal control

Published online by Cambridge University Press:  12 September 2017

Tingting Wu ,
David Z. W. Wang ,
Zhengmeng Jin  and
Jun Zhang
Tingting Wu*
Affiliation:
School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, 210023, China College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China
David Z. W. Wang
Affiliation:
School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore
Zhengmeng Jin
Affiliation:
College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China
Jun Zhang
Affiliation:
College of Science, Nanchang Institute of Technology, Nanchang, 330099, Jiangxi, China
*
*Corresponding author. Email address:[email protected] (T. T. Wu)
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Abstract

High order total variation (TV2) and ℓ1 based (TV2L1) model has its advantage over the TVL1 for its ability in avoiding the staircase; and a constrained model has the advantage over its unconstrained counterpart for simplicity in estimating the parameters. In this paper, we consider solving the TV2L1 based magnetic resonance imaging (MRI) signal reconstruction problem by an efficient alternating direction method of multipliers. By sufficiently utilizing the problem's special structure, we manage to make all subproblems either possess closed-form solutions or can be solved via Fast Fourier Transforms, which makes the cost per iteration very low. Experimental results for MRI reconstruction are presented to illustrate the effectiveness of the new model and algorithm. Comparisons with its recent unconstrained counterpart are also reported.

Keywords

Magnetic resonance imaging (MRI)high order total variationalternating direction method of multipliers (ADMM)constrained model

MSC classification

Secondary: 90C25: Convex programming 49M27: Decomposition methods 68U10: Image processing
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 4 , November 2017 , pp. 895 - 912
Copyright
Copyright © Global-Science Press 2017 

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