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 …

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 …

Total variation regularization has proven to be a valuable tool in the context of optimal
control of differential equations. This is particularly attributed to the observation that TV …

This article discusses nonconforming finite element methods for convex minimization
problems and systematically derives dual mixed formulations. Duality relations lead to …

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 …

Based on the Fenchel duality we build a primal-dual framework for minimizing a general
functional consisting of a combined L 1 and L 2 data-fidelity term and a scalar or vectorial …

This paper gives a unified convergence analysis of additive Schwarz methods for general
convex optimization problems. Resembling the fact that additive Schwarz methods for linear …

This paper addresses a general problem of computing inversion-free maps between
continuous and discrete domains that induce minimal geometric distortions. We will refer to …

We present a scalable and efficient framework for the inference of spatially-varying
parameters of continuum materials from image observations of their deformations. Our goal …

Total variation integer optimal control problems admit solutions and necessary optimality
conditions via geometric variational analysis. In spite of the existence of said solutions …