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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/939131 |
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| _version_ | 1832567460659724288 |
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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. |
| format | Article |
| id | doaj-art-910971cfe596419f8a23d9528f06023b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT elishaachiengogada analternativevariationalframeworkforimagedenoising AT zhichangguo analternativevariationalframeworkforimagedenoising AT boyingwu analternativevariationalframeworkforimagedenoising AT elishaachiengogada alternativevariationalframeworkforimagedenoising AT zhichangguo alternativevariationalframeworkforimagedenoising AT boyingwu alternativevariationalframeworkforimagedenoising |