Image Processing Based on Fractional Partial Differential Equations
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Date
2024-06
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
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.
Description
Keywords
Image processing, Linear and non-linear diffusion, Existence, Uniqueness, CaputoFabrizio fractional derivative, Finite difference approximations