Discrete total variation with finite elementsMS64

The total-variation (TV) seminorm is ubiquitous as a regularizing functional in image analysis and related applications. We propose and analyze a discrete analog of the TV-seminorm for functions belonging to a space of globally discontinuous or continuous finite element functions on a geometrically conforming mesh. We show that our discrete TV functional admits a dual representation close to the continuous formulation and allows for efficient implementations of classical image restoration algorithms.

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

Roland Herzog (Technische Universität Chemnitz)
Marc Herrmann (University of Würzburg)
Stephan Schmidt (University of Würzburg)
José Vidal Núñez (Technische Universität Chemnitz)
Gerd Wachsmuth (Technische Universität Chemnitz)