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Fast Algorithms for the Anisotropic LLT Model in Image Denoising

Published online by Cambridge University Press:  28 May 2015

Zhi-Feng Pang ,
Li-Lian Wang  and
Yu-Fei Yang
Zhi-Feng Pang*
Affiliation:
College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Li-Lian Wang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
Yu-Fei Yang*
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
*
Corresponding author. Email: zhifengpang@163.com
Corresponding author. Email: lilian@ntu.edu.sg
Corresponding author. Email: yfyang@hnu.edu.cn
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Abstract

In this paper, we propose a new projection method for solving a general minimization problems with two L1-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rate O(k−2). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.

Keywords

65M1078A48Image denoisinganisotropic LLT modelDouglas-Rachford splitting methodsplit Bregman methodprojection methodfast projection method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011 , pp. 264 - 283
Copyright
Copyright © Global-Science Press 2011

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