Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers. Issue 4 (12th September 2017)

• Record Type: Journal Article
• Authors: Wu, Tingting; Wang, David Z. W.; Jin, Zhengmeng; Zhang, Jun
• Is Part Of: Numerical mathematics. Volume 10:Issue 4(2017)
• Page Start: 895
• Page End: 912
• Publication Date: 2017-09-12
• Subjects: 90C25, -- 49M27, -- 68U10; Magnetic resonance imaging (MRI), -- high order total variation, -- alternating direction method of multipliers (ADMM), -- constrained model; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.m1664
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: High order total variation (TV2) and ℓ 1 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.