Discontinuous Galerkin Method for Total Variation Minimization on one-dimensional Inpainting Problem

TL;DR

This paper compares finite element and discontinuous Galerkin methods for total variation minimization in 1D gray-scale inpainting, demonstrating their effectiveness through numerical examples.

Contribution

It introduces the application of discontinuous Galerkin methods to total variation minimization in 1D inpainting problems, providing a comparative analysis with finite element methods.

Findings

Discontinuous Galerkin method effectively minimizes total variation in 1D inpainting.

Numerical examples show different image recovery results between the two methods.

The study demonstrates the practical applicability of DG methods for BV function minimization.

Abstract

This paper is concerned with the numerical minimization of energy functionals in $BV(\Omega)$ (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.