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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 834035, 13 pages
http://dx.doi.org/10.1155/2013/834035
Research Article

A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal

1School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu 222005, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 17 October 2012; Revised 10 March 2013; Accepted 13 March 2013

Academic Editor: Fatih Yaman

Copyright © 2013 Xiao-Guang Lv et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Multiplicative noise removal problem has received considerable attention in recent years. The total variation regularization method for the solution of the noise removal problem can preserve edges well but has the sometimes undesirable staircase effect. In this paper, we propose a fast high-order total variation minimization method to restore multiplicative noisy images. The proposed method is able to preserve edges and at the same time avoid the staircase effect in the smooth regions. An alternating minimization algorithm is employed to solve the proposed high-order total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Some numerical results show that the proposed method gives restored images of higher quality than some existing multiplicative noise removal methods.