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

This paper is concerned with the numerical minimization of energy functionals in $BV(\mathrm{\Omega })$ (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.