Image Processing Based on Fractional Partial Differential Equations

Abstract

This work presents a fractional diffusion model, which modifies the Perona-Malik model by incorporating the Caputo-Fabrizio fractional gradient into the diffusivity function. A theoretical investigation was conducted to examine the existence and uniqueness of the solution. Additionally, we carried out a numerical study, enabling us to perform experiments that confirmed the model’s effectiveness in noise reduction and edge preservation. This also allowed us to compare our results with those of the classical Perona-Malik model.