A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise
Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/1/64 |
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| author | Xiangyu Bai Dazhi Zhang Shengzhu Shi Wenjuan Yao Zhichang Guo Jiebao Sun |
| author_facet | Xiangyu Bai Dazhi Zhang Shengzhu Shi Wenjuan Yao Zhichang Guo Jiebao Sun |
| author_sort | Xiangyu Bai |
| collection | DOAJ |
| description | Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative is imposed due to its textural detail enhancing capability. We also introduce the gray level indicator, which fully considers the gray level information of multiplicative noise images, so that the model can effectively remove high level noise and protect the details of the structure. The well-posedness of the proposed fractional-order telegraph diffusion model is presented by applying the Schauder’s fixed-point theorem. To solve the model, we develop an iterative algorithm based on the discrete Fourier transform in the frequency domain. We give various numerical results on despeckling natural and real SAR images. The experiments demonstrate that the proposed method can remove multiplicative noise and preserve texture well. |
| first_indexed | 2024-03-09T12:39:30Z |
| format | Article |
| id | doaj.art-0afe7ac5346444709ecb9fd05d3f1356 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T12:39:30Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-0afe7ac5346444709ecb9fd05d3f13562023-11-30T22:19:47ZengMDPI AGFractal and Fractional2504-31102023-01-01716410.3390/fractalfract7010064A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative NoiseXiangyu Bai0Dazhi Zhang1Shengzhu Shi2Wenjuan Yao3Zhichang Guo4Jiebao Sun5School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaMultiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative is imposed due to its textural detail enhancing capability. We also introduce the gray level indicator, which fully considers the gray level information of multiplicative noise images, so that the model can effectively remove high level noise and protect the details of the structure. The well-posedness of the proposed fractional-order telegraph diffusion model is presented by applying the Schauder’s fixed-point theorem. To solve the model, we develop an iterative algorithm based on the discrete Fourier transform in the frequency domain. We give various numerical results on despeckling natural and real SAR images. The experiments demonstrate that the proposed method can remove multiplicative noise and preserve texture well.https://www.mdpi.com/2504-3110/7/1/64multiplicative noise removaltexturefractional-ordertelegraph diffusion |
| spellingShingle | Xiangyu Bai Dazhi Zhang Shengzhu Shi Wenjuan Yao Zhichang Guo Jiebao Sun A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise Fractal and Fractional multiplicative noise removal texture fractional-order telegraph diffusion |
| title | A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise |
| title_full | A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise |
| title_fullStr | A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise |
| title_full_unstemmed | A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise |
| title_short | A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise |
| title_sort | fractional order telegraph diffusion model for restoring texture images with multiplicative noise |
| topic | multiplicative noise removal texture fractional-order telegraph diffusion |
| url | https://www.mdpi.com/2504-3110/7/1/64 |
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