Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image
The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for t...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/483791 |
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| author | Yi-Fei Pu Ji-Liu Zhou Patrick Siarry Ni Zhang Yi-Guang Liu |
| author_facet | Yi-Fei Pu Ji-Liu Zhou Patrick Siarry Ni Zhang Yi-Guang Liu |
| author_sort | Yi-Fei Pu |
| collection | DOAJ |
| description | The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images. |
| format | Article |
| id | doaj-art-0f0b3f2b1de6400caf3ad00cea753461 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0f0b3f2b1de6400caf3ad00cea7534612025-02-03T01:32:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/483791483791Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture ImageYi-Fei Pu0Ji-Liu Zhou1Patrick Siarry2Ni Zhang3Yi-Guang Liu4School of Computer Science and Technology, Sichuan University, Chengdu 610065, ChinaSchool of Computer Science and Technology, Sichuan University, Chengdu 610065, ChinaUniversité de Paris 12 (LiSSi, E.A. 3956), 61 avenue du Général de Gaulle, 94010 Créteil Cedex, FranceLibrary of Sichuan University, Chengdu 610065, ChinaSchool of Computer Science and Technology, Sichuan University, Chengdu 610065, ChinaThe traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.http://dx.doi.org/10.1155/2013/483791 |
| spellingShingle | Yi-Fei Pu Ji-Liu Zhou Patrick Siarry Ni Zhang Yi-Guang Liu Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image Abstract and Applied Analysis |
| title | Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image |
| title_full | Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image |
| title_fullStr | Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image |
| title_full_unstemmed | Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image |
| title_short | Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image |
| title_sort | fractional partial differential equation fractional total variation and fractional steepest descent approach based multiscale denoising model for texture image |
| url | http://dx.doi.org/10.1155/2013/483791 |
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