Some applications of partial differential equations in medical image processing

Bassam Al-Hamzah, Fahmi Al-Hamzah

Article ID: 3148
Vol 3, Issue 2, 2025
DOI: https://doi.org/10.54517/mss3148
Received: 9 December 2024; Accepted: 6 February 2025; Available online: 8 April 2025; Issue release: 30 June 2025


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Abstract

The second-order nonlinear diffusion parabolic partial differential equations models have been widely applied in image restoration. However, the numerical results in the literature treat only the case without source term. In this paper, we have developed a general calculation code which is based in a consistent explicit approximation finite difference method scheme. Furthermore, the paper provides satisfying answers with a nonlinear source term relying on the image solution and its gradient. Numerical experiments are presented to show the robustness of the cases with source term to obtain better results in image denoising restoration using measures as Peak Signal-to-Noise Ratio (PSNR) and SNR of filtering and noisy image.

Keywords

nonlinear parabolic; reaction-diffusion; medical image processing


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