Piecewise Linear Approximation of the Continuous Rudin--Osher--Fatemi Model for Image Denoising

Abstract

This paper is concerned with the numerical approximation of the minimizer of the continuous Rudin--Osher--Fatemi (ROF) model for image denoising. A new discrete total variation is proposed and the associated Hilbertian total variation denoising model is used to construct continuous piecewise linear functions that approximate the minimizer of the ROF model in the strong topology of $L^2(\Omega)$, provided that the data function is bounded and weakly regular in the sense of $\text{Lip}(\alpha,\text{L}^2(\Omega))$.