On an image denoising model based on Atangana–Baleanu fractional derivative

Image denoising remains a significant challenge in image processing, as noise can degrade image quality during acquisition or transmission. In this work, we propose a new image denoising model based on the Atangana–Baleanu fractional derivative, introducing tunable parameters to control the regularization process. This model generalizes the well-known Rudin–Osher–Fatemi (ROF), Perona–Malik (PM), and Liao–Feng (LF) methods and can be viewed as a constrained optimization problem, extending the total variation approach. We provide a detailed demonstration of the finite difference scheme for the Atangana–Baleanu derivative and prove the theoretical stability of the numerical method. We also propose several simulations to optimally select the model parameters, especially the fractional derivative order α and the explicit–implicit parameter θ. Experimental results show that our approach effectively reduces noise and preserves image structure in both natural and medical images, outperforming existing models in terms of PSNR and SSIM values.