Implementation of a nonlinear anisotropic image denoising model in FEniCS

In this talk, we present a numerical implementation of the following nonlinear anisotropic diffusion-based image denoising model, using the computing platform FEniCS Project:

$$ u-u_{0} = \frac{1}{2 \lambda} \operatorname{div} \left(\frac{1}{\left(\epsilon^2+\vert \nabla u_\sigma \vert^2\right)^{1-p/2}}\nabla u \right) \qquad \text{in } \Omega,$$

$$\partial_n u = 0 \qquad \text{on } \partial\Omega.$$

\(u=u(x,y)\) denotes the unknown image to be recovered, \(u_{0}\) is the observed noisy image, \(\Omega \subset \mathbb{R}^{2}\) is the spatial image domain and \(\partial_{n} u\) denotes the derivative of \(u\) in the direction normal to the boundary \(\partial \Omega\).

We also compare the numerical results with those obtained using finite difference method.