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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 5130346, 12 pages
Research Article

A Cartoon-Texture Decomposition Based Multiplicative Noise Removal Method

1School of Mathematics and Statistics, Xidian University, Xi’an 710026, China
2School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang 453003, China

Received 23 April 2016; Revised 29 June 2016; Accepted 26 July 2016

Academic Editor: Maria L. Gandarias

Copyright © 2016 Chenping Zhao 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.


We propose a new frame for multiplicative noise removal. To improve the multiplicative denoising performance, we add the regularization of texture component in the denoising model, designing a multiscale multiplicative noise removal model. The proposed model is jointly convex and can be easily solved by optimization algorithms. We introduce Douglas-Rachford splitting method to solve the proposed model. In the algorithm, we make full use of some important proximity operators, which have closed expression or can be executed in one time iteration. In particular, the proximity of norm is deduced, which is just the Fourier domain filtering. In the process of simulation experiments, we first analyze and select the needed parameters and then test the experiments on several images using the designed algorithm and the given parameters. Finally, we compare the denoising performance of the proposed model with the existing models, in which the signal to noise ratio (SNR) and the peak signal to noise ratios (PSNRs) are applied to evaluate the noise suppressing effects. Experimental results demonstrate that the designed algorithms can solve the model perfectly and the recovery images of the proposed model have higher SNRs/PSNRs and better visual quality.