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An Algorithm for the Proximity Operator in Hybrid TV-Wavelet Regularization, with Application to MR Image Reconstruction

Published online by Cambridge University Press:  28 May 2015

Yu-Wen Fang ,
Xiao-Mei Huo  and
You-Wei Wen
Yu-Wen Fang
Affiliation:
Faculty of Science, Kunming University of Science and Technology, Yunnan, China
Xiao-Mei Huo
Affiliation:
Faculty of Science, Kunming University of Science and Technology, Yunnan, China
You-Wei Wen*
Affiliation:
Faculty of Science, Kunming University of Science and Technology, Yunnan, China
*
Corresponding author. Email: wenyouwei@gmail.com
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Abstract

Total variation (TV) and wavelet L1 norms have often been used as regularization terms in image restoration and reconstruction problems. However, TV regularization can introduce staircase effects and wavelet regularization some ringing artifacts, but hybrid TV and wavelet regularization can reduce or remove these drawbacks in the reconstructed images. We need to compute the proximal operator of hybrid regularizations, which is generally a sub-problem in the optimization procedure. Both TV and wavelet L1 regularisers are nonlinear and non-smooth, causing numerical difficulty. We propose a dual iterative approach to solve the minimization problem for hybrid regularizations and also prove the convergence of our proposed method, which we then apply to the problem of MR image reconstruction from highly random under-sampled k-space data. Numerical results show the efficiency and effectiveness of this proposed method.

Keywords

65K1068U10Total Variation (TV)waveletregularizationMR image
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 1 , February 2014 , pp. 21 - 34
Copyright
Copyright © Global-Science Press 2014

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