We present a fully computable a posteriori error estimate for the finite element approximation of the Rudin-Osher-Fatemi problem. We propose an adaptive refinement strategy relying on the fact that the primal-dual gap controls the $L^2$-error between the solution and an FE-approximation and on an accurate conforming discretization of both the primal and the dual problem and reliable iterative solution techniques. Numerical experiments show a significant improvement over approximations on uniformly refined triangulations.

This presentation is part of Minisymposium “MS64 - Images and Finite Elements”
organized by: Roland Herzog (Technische Universität Chemnitz) , Stephan Schmidt (University of Würzburg) .

Authors:

Sören Bartels (University of Freiburg)

Marijo Milicevic (University of Freiburg)

Keywords:

adaptivity, error estimation, nonlinear optimization, total variation