This article studies the denoising performance of total variation (TV) image regularization.
More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher …

This work is concerned with the determination of the diffusion coefficient from distributed
data of the state. This problem is related to homogenization theory on the one hand and to …

A new method for performing density-based topology optimization for Stokes flow is
presented. It differs from previous approaches in the way the underlying mixed integer …

In this article we characterize the $\mathrm {L}^\infty $ eigenvalue problem associated to the
Rayleigh quotient $\left.{\|\nabla u\| _ {\mathrm {L}^\infty}}\middle/{\| u\| _\infty}\right. $ and …

In this work, we introduce a function space setting for a wide class of structural/weighted total
variation (TV) regularization methods motivated by their applications in inverse problems. In …

The purpose of the present chapter is to bind together and extend some recent
developments regarding data-driven nonsmooth regularization techniques in image …

We analyse the functional 𝒥 (u)=∥∇ u∥∞ defined on Lipschitz functions with
homogeneous Dirichlet boundary conditions. Our analysis is performed directly on the …

Modeling magnitude magnetic resonance images (MRI) Rician denoising in a Bayesian or
generalized Tikhonov framework using total variation (TV) leads naturally to the …

It is well-known that point sources with sufficient mutual distance can be reconstructed
exactly from finitely many Fourier measurements by solving a convex optimization problem …

Optimal control problems for semilinear elliptic equations with control costs in the space of
bounded variations are analysed. BV-based optimal controls favor piecewise constant, and …