## Abstract and Applied Analysis

### An Alternative Variational Framework for Image Denoising

#### Abstract

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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 939131, 16 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278112

Digital Object Identifier
doi:10.1155/2014/939131

Mathematical Reviews number (MathSciNet)
MR3208575

Zentralblatt MATH identifier
07023354

#### Citation

Ogada, Elisha Achieng; Guo, Zhichang; Wu, Boying. An Alternative Variational Framework for Image Denoising. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 939131, 16 pages. doi:10.1155/2014/939131. https://projecteuclid.org/euclid.aaa/1412278112

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