The Convergence of a Central-Difference Discretization of Rudin-Osher-Fatemi Model for Image Denoising

摘要

We study the connection between minimizers of the discrete and the continuous Rudin-Osher-Fatemi models. We use a central-difference total variation term in the discrete ROF model and treat the discrete input data as a projection of the continuous input data into the discrete space. We employ a method developed in [13] with slight adaption to the setting of the central-difference total variation ROF model. We obtain an error bound between the discrete and the continuous min-imizer in L~2 norm under the assumption that the continuous input data are in W~(1,2).