Automated Finite Element Solution of Diffusion Models for Image Denoising

We present in this paper a numerical solution of a generalized diffusion-based image denoising model, using the finite element computing platform FEniCS. The generalized model contains as special cases three classical denoising techniques: linear isotropic diffusion, total variation, and Perona-Malik method. The numerical simulation using four classical grayscale images demonstrates the superior performance of the finite element method over the finite difference method in terms of both the denoising quality and the computational work.