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Majee, S., Brännström, Å., & Lundstrom, N. (2025). Well-posedness of a variable-exponent telegraph equation applied to image despeckling. Evolution Equations and Control Theory 10.3934/eect.2025039. (In Press)
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Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Image despeckling, nonlinear diffusion, telegraph equation, variable exponent, gray level function, weak solution |
| Research Programs: | Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Cooperation and Transformative Governance (CAT) Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM) |
| Depositing User: | Luke Kirwan |
| Date Deposited: | 02 Jun 2025 07:47 |
| Last Modified: | 02 Jun 2025 07:47 |
| URI: | https://pure.iiasa.ac.at/20637 |
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