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East Asian Journal on Applied Mathematics, 1 (2011), pp. 264-283. |
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Fast Algorithms for the Anisotropic LLT Model in Image Denoising Zhi-Feng Pang 1, Li-Lian Wang 2*, Yu-Fei Yang 3 1 College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China and Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore.2 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore. 3 College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China. Received 23 December 2010; Accepted (in revised version) 26 April 2011 Available online 27 July 2011 doi:10.4208/eajam.231210.260411a Abstract In this paper, we propose a new projection method for solving a general minimization problems with two $L^1$-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. AMS subject classifications: 65M10, 78A48 Key words: Image denoising, anisotropic LLT model, Douglas-Rachford splitting method, split Bregman method, projection method, fast projection method. *Corresponding author. Email: zhifengpang@163.com (Z.-F. Pang), lilian@ntu.edu.sg (L.-L. Wang), yfyang@hnu.edu.cn (Y.-F. Yang) |