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Mathematical Problems in Engineering
Volume 2017, Article ID 9370984, 10 pages
Research Article

Multiplicative Noise Removal Based on the Linear Alternating Direction Method for a Hybrid Variational Model

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
2School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China
3Institute of Graphics and Image Processing, Xianyang Normal University, Xianyang 712000, China

Correspondence should be addressed to Jianlou Xu; moc.621@uolnaijux

Received 6 January 2017; Accepted 7 March 2017; Published 15 May 2017

Academic Editor: Pasquale Memmolo

Copyright © 2017 Yan Hao 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.


To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.