An Alternative Variational Framework for Image Denoising

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 consid...

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Main Authors: Elisha Achieng Ogada, Zhichang Guo, Boying Wu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/939131
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author Elisha Achieng Ogada
Zhichang Guo
Boying Wu
author_facet Elisha Achieng Ogada
Zhichang Guo
Boying Wu
author_sort Elisha Achieng Ogada
collection DOAJ
description 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.
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institution Kabale University
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publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-910971cfe596419f8a23d9528f06023b2025-02-03T01:01:28ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/939131939131An Alternative Variational Framework for Image DenoisingElisha Achieng Ogada0Zhichang Guo1Boying Wu2Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, 150001, ChinaWe 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.http://dx.doi.org/10.1155/2014/939131
spellingShingle Elisha Achieng Ogada
Zhichang Guo
Boying Wu
An Alternative Variational Framework for Image Denoising
Abstract and Applied Analysis
title An Alternative Variational Framework for Image Denoising
title_full An Alternative Variational Framework for Image Denoising
title_fullStr An Alternative Variational Framework for Image Denoising
title_full_unstemmed An Alternative Variational Framework for Image Denoising
title_short An Alternative Variational Framework for Image Denoising
title_sort alternative variational framework for image denoising
url http://dx.doi.org/10.1155/2014/939131
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AT zhichangguo analternativevariationalframeworkforimagedenoising
AT boyingwu analternativevariationalframeworkforimagedenoising
AT elishaachiengogada alternativevariationalframeworkforimagedenoising
AT zhichangguo alternativevariationalframeworkforimagedenoising
AT boyingwu alternativevariationalframeworkforimagedenoising