TY - JOUR T1 - A Total Variation Discontinuous Galerkin Approach for Image Restoration JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 81 EP - 93 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/479.html KW - Discontinuous Galerkin methods, total variation image denoising, energy minimization methods, nonlinear elliptic filters. AB -

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.