Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives
A fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising. However, determining the appropriate order requires numerous ex...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5581944 |
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| _version_ | 1832547019025022976 |
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| author | Xiaoran Lin Yachao Wang Guohao Wu Jing Hao |
| author_facet | Xiaoran Lin Yachao Wang Guohao Wu Jing Hao |
| author_sort | Xiaoran Lin |
| collection | DOAJ |
| description | A fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising. However, determining the appropriate order requires numerous experiments, and different image regions using the same order may cause too much smoothing or insufficient denoising. Thus, we propose an adaptive fractional integral operator based on the Atangana–Baleanu derivatives. Edge intensity, global entropy, local entropy, and local variance weights are used to construct an adaptive order function that can adapt to changes in different regions of an image. Then, we use the adaptive order function to improve the masks based on the Grumwald–Letnikov scheme (GL_ABC) and Toufik–Atangana scheme (TA_ABC), namely, Ada_GL_ABC and Ada_TA_ABC, respectively. Finally, multiple evaluation indicators are used to assess the proposed masks. The experimental results demonstrate that the proposed adaptive operator can better preserve texture details when denoising than other similar operators. Furthermore, the image processed by the Ada_TA_ABC operator has less noise and more detail, which means the proposed adaptive function has universality. |
| format | Article |
| id | doaj-art-792ec72118b24db1bc498a6cb1136007 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-792ec72118b24db1bc498a6cb11360072025-02-03T06:46:14ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55819445581944Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu DerivativesXiaoran Lin0Yachao Wang1Guohao Wu2Jing Hao3College of Information Technology, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, ChinaCollege of Information Technology, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, ChinaCollege of Computer Science, Chongqing University, Chongqing 40044, ChinaCollege of Information Technology, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, ChinaA fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising. However, determining the appropriate order requires numerous experiments, and different image regions using the same order may cause too much smoothing or insufficient denoising. Thus, we propose an adaptive fractional integral operator based on the Atangana–Baleanu derivatives. Edge intensity, global entropy, local entropy, and local variance weights are used to construct an adaptive order function that can adapt to changes in different regions of an image. Then, we use the adaptive order function to improve the masks based on the Grumwald–Letnikov scheme (GL_ABC) and Toufik–Atangana scheme (TA_ABC), namely, Ada_GL_ABC and Ada_TA_ABC, respectively. Finally, multiple evaluation indicators are used to assess the proposed masks. The experimental results demonstrate that the proposed adaptive operator can better preserve texture details when denoising than other similar operators. Furthermore, the image processed by the Ada_TA_ABC operator has less noise and more detail, which means the proposed adaptive function has universality.http://dx.doi.org/10.1155/2021/5581944 |
| spellingShingle | Xiaoran Lin Yachao Wang Guohao Wu Jing Hao Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives Journal of Mathematics |
| title | Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives |
| title_full | Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives |
| title_fullStr | Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives |
| title_full_unstemmed | Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives |
| title_short | Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives |
| title_sort | image denoising of adaptive fractional operator based on atangana baleanu derivatives |
| url | http://dx.doi.org/10.1155/2021/5581944 |
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