TY - JOUR
T1 - Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers
AU - Tingting Wu, David Z. W. Wang, Zhengmeng Jin & Jun Zhang
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 - <p style="text-align: justify;">High order total variation (TV<sup>2</sup>) and ℓ<sub>1</sub> 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&#39;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.</p>