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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912373, 21 pages
Research Article

A Convex Adaptive Total Variation Model Based on the Gray Level Indicator for Multiplicative Noise Removal

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 28 March 2013; Accepted 14 May 2013

Academic Editor: Guoyin Li

Copyright © 2013 Gang Dong 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.


This paper focuses on the problem of multiplicative noise removal. Using a gray level indicator, we derive a new functional which consists of the adaptive total variation term and the global convex fidelity term. We prove the existence, uniqueness, and comparison principle of the minimizer for the variational problem. The existence, uniqueness, and long-time behavior of the associated evolution equation are established. Finally, experimental results illustrate the effectiveness of the model in multiplicative noise reduction. Different from the other methods, the parameters in the proposed algorithms are found dynamically.