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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 939131, 16 pages
Research Article

An Alternative Variational Framework for Image Denoising

1Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
2Department of Mathematics, Egerton University, Egerton, Kenya

Received 13 March 2014; Accepted 6 April 2014; Published 5 May 2014

Academic Editor: Carlos Lizama

Copyright © 2014 Elisha Achieng Ogada 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 an alternative framework for total variation based image denoising models. The model is based on the minimization of the total variation with a functional coefficient, where, in this case, the functional coefficient is a function of the magnitude of image gradient. We determine the considerations to bear on the choice of the functional coefficient. With the use of an example functional, we demonstrate the effectiveness of a model chosen based on the proposed consideration. In addition, for the illustrative model, we prove the existence and uniqueness of the minimizer of the variational problem. The existence and uniqueness of the solution associated evolution equation are also established. Experimental results are included to demonstrate the effectiveness of the selected model in image restoration over the traditional methods of Perona-Malik (PM), total variation (TV), and the D-α-PM method.