gradient-weighted diffusion pde for image denoising

This paper presents a mathematical model based on a gradient-weighted diffusion partial differential equation for image denoising. both the diffusion and fidelity terms are locally adapted according to the image gradient, allowing selective smoothing while preserving edges. the adaptive fidelity reduces over-smoothing near strong gradients and maintains closeness to the original image. experiments on standard test images confirm that the proposed approach achieves improved denoising performance compared to conventional diffusion-based models when evaluated by common quality measures.