A Total Variation Model Based on the Strictly Convex Modification for Image Denoising
We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behav...
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| Main Authors: | , , , |
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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/10.1155/2014/948392 |
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| _version_ | 1832551576456134656 |
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| author | Boying Wu Elisha Achieng Ogada Jiebao Sun Zhichang Guo |
| author_facet | Boying Wu Elisha Achieng Ogada Jiebao Sun Zhichang Guo |
| author_sort | Boying Wu |
| collection | DOAJ |
| description | We propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV), the Perona-Malik (PM), and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one. |
| format | Article |
| id | doaj-art-02d3a1d75c62497e94fbae5e8ffcf2f1 |
| 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-02d3a1d75c62497e94fbae5e8ffcf2f12025-02-03T06:00:57ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/948392948392A Total Variation Model Based on the Strictly Convex Modification for Image DenoisingBoying Wu0Elisha Achieng Ogada1Jiebao Sun2Zhichang Guo3Department 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, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe propose a strictly convex functional in which the regular term consists of the total variation term and an adaptive logarithm based convex modification term. We prove the existence and uniqueness of the minimizer for the proposed variational problem. The existence, uniqueness, and long-time behavior of the solution of the associated evolution system is also established. Finally, we present experimental results to illustrate the effectiveness of the model in noise reduction, and a comparison is made in relation to the more classical methods of the traditional total variation (TV), the Perona-Malik (PM), and the more recent D-α-PM method. Additional distinction from the other methods is that the parameters, for manual manipulation, in the proposed algorithm are reduced to basically only one.http://dx.doi.org/10.1155/2014/948392 |
| spellingShingle | Boying Wu Elisha Achieng Ogada Jiebao Sun Zhichang Guo A Total Variation Model Based on the Strictly Convex Modification for Image Denoising Abstract and Applied Analysis |
| title | A Total Variation Model Based on the Strictly Convex Modification for Image Denoising |
| title_full | A Total Variation Model Based on the Strictly Convex Modification for Image Denoising |
| title_fullStr | A Total Variation Model Based on the Strictly Convex Modification for Image Denoising |
| title_full_unstemmed | A Total Variation Model Based on the Strictly Convex Modification for Image Denoising |
| title_short | A Total Variation Model Based on the Strictly Convex Modification for Image Denoising |
| title_sort | total variation model based on the strictly convex modification for image denoising |
| url | http://dx.doi.org/10.1155/2014/948392 |
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