Nonlocal -Laplacian involving a nonlinear fractional reaction-diffusion system applied to image restoration

Image restoration has been a longstanding challenge in image processing, involving the enhancement of image content to extract valuable information. Nonlinear models have demonstrated their efficacy in eliminating additive noise, which motivates our goal of investigating a novel nonlocal nonlinear reaction-diffusion model for noise removal. The proposed model integrates a fractional diffusion equation with a nonlinear nonlocal rho-Laplace operator, with the fidelity term employing a weak norm to better capture oscillatory patterns and intricate details in textured images. Using the Schauder fixed point theorem, the well-posedness of the proposed model solution is established. The experimental results confirm the effectiveness and efficiency of the proposed model, providing validation for its practical utility.