Over the last decades, the total variation (TV) has evolved to be one of the most broadly-
used regularisation functionals for inverse problems, in particular for imaging applications …

Denoising is the problem of removing noise from an image. The most commonly studied
case is with additive white Gaussian noise (AWGN), where the observed noisy image f is …

We present a primal-dual method to solve L^1-type nonsmooth optimization problems
independently of the grid size. We apply these results to two important problems: the Rudin …

In this work, we study a general framework of discrete approximations of the total variation
for image reconstruction problems. The framework, for which we can show consistency in …

The numerical solution of a convex minimization problem involving the nonsmooth total
variation norm is analyzed. Consistent finite element discretizations that avoid …

In this paper we study finite-difference approximations to the variational problem using the
bounded variation (BV) smoothness penalty that was introduced in an image smoothing …

We present and compare various types of discretizations which have been proposed to
approximate the total variation (mostly, of a gray-level image in two dimensions). We discuss …

This paper deals with the so-called staircasing phenomenon, which frequently arises in total
variation-based denoising models in image analysis. We prove in particular that staircasing …

We propose an adaptive implementation of a Crouzeix–Raviart-based discretization of the
total variation, which has the property of approximating from below the total variation, with …

We present a convergence rate analysis of the Rudin–Osher–Fatemi (ROF) denoising
problem for two different discretizations of the total variation. The first is the standard …