IMAGE PROCESSING BY MEANS OF A LINEAR INTEGRO-DIFFERENTIAL EQUATION

摘要

Partial differential equations (PDE) have been considered in image processing for denoising and stabilizing edges. Main approaches concern to diffusion processes (heat equation) and variational principles (energy method). In this work we propose a first approach to image processing by means of integro-differential equations of fractional order. Qur purpose is to exploit properties of the solution of the linear fractional integro-differential equation, with special regard to regularization processes. Some of these properties can be considered as intermediate between those of the heat equation and the ones of the wave equation. Practical illustrations are provided using suitable numerical methods, thoses combine both fractional quadrature rules (FQR) (or Gruenwald-Letnikov rules), and classical numerical schemes.