Volume 10, Issue 4
Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers

Tingting Wu, David Z. W. Wang, Zhengmeng Jin & Jun Zhang

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 895-912.

Published online: 2017-11

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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 variation, alternating direction method of multipliers (ADMM), constrained model.

  • AMS Subject Headings

90C25, 49M27, 68U10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-10-895, author = {}, title = {Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {4}, pages = {895--912}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1664}, url = {http://global-sci.org/intro/article_detail/nmtma/10461.html} }
TY - JOUR T1 - Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 895 EP - 912 PY - 2017 DA - 2017/11 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1664 UR - https://global-sci.org/intro/article_detail/nmtma/10461.html KW - Magnetic resonance imaging (MRI), high order total variation, alternating direction method of multipliers (ADMM), constrained model. AB -

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.

Tingting Wu, David Z. W. Wang, Zhengmeng Jin & Jun Zhang. (2019). Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers. Numerical Mathematics: Theory, Methods and Applications. 10 (4). 895-912. doi:10.4208/nmtma.2017.m1664
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