Numerical analysis of some time-fractional partial differential equations for noise removal

Abstract

In this paper, we consider the numerical resolution of two time-fractional partial differential equations for processing image denoising, which are obtained from some classical partial differential equations for processing image denoising, edge preservation and compression by replacing the first-order time derivative with a fractional derivative of order α, with 0 < α < 1. Discrete schemes of these models are introduced based on the finite differences method. Then, stability and error estimates are derived on the approximate solutions. Numerical experiments are presented to show the robustness of these new time-fractional models to obtain better results in image denoising and restoration.