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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08175 |
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| _version_ | 1866912116877819904 |
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| author | Majee, Sudeb Brännström, Åke Lundström, Niklas L. P. |
| author_facet | Majee, Sudeb Brännström, Åke Lundström, Niklas L. P. |
| contents | In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable exponents for edge detection. All of these depend on the gray level of the image or its gradient. We rigorously prove the existence and uniqueness of weak solutions of our model in a functional setting and perform numerical experiments to assess how well it can despeckle noisy gray-level images. We consider both a range of natural images contaminated by varying degrees of artificial speckle noise and synthetic aperture radar (SAR) images. We finally compare our method with the nonlocal speckle removal technique and find that our model outperforms the latter at speckle elimination and edge preservation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of a Variable-Exponent Telegraph Equation Applied to Image Despeckling Majee, Sudeb Brännström, Åke Lundström, Niklas L. P. Analysis of PDEs Numerical Analysis 35L70, 65M06, 68U10 In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable exponents for edge detection. All of these depend on the gray level of the image or its gradient. We rigorously prove the existence and uniqueness of weak solutions of our model in a functional setting and perform numerical experiments to assess how well it can despeckle noisy gray-level images. We consider both a range of natural images contaminated by varying degrees of artificial speckle noise and synthetic aperture radar (SAR) images. We finally compare our method with the nonlocal speckle removal technique and find that our model outperforms the latter at speckle elimination and edge preservation. |
| title | Well-posedness of a Variable-Exponent Telegraph Equation Applied to Image Despeckling |
| topic | Analysis of PDEs Numerical Analysis 35L70, 65M06, 68U10 |
| url | https://arxiv.org/abs/2411.08175 |