A Total Variation Discontinuous Galerkin Approach for Image Restoration
Keywords:
Discontinuous Galerkin methods, total variation image denoising, energy minimization methods, nonlinear elliptic filters.Abstract
The focal point of this paper is to propose and analyze a $\mathbb{P}_0$ discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.