Variational Methods for the Reconstruction of Signals with Discontinuities

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Title: Variational Methods for the Reconstruction of Signals with Discontinuities
Authors: Weinmann, Andreas
Abstract: We here summarize the content of the publications comprising this thesis. The chapter is organized as follows. We start out by briefly giving motivation for the considered problems and by reviewing the state of the art in Chapter 2.1. Here, we consider data living in linear space and in manifolds as well as the direct and indirect measurement case. In the rest of the chapter, we summarize the contributions of this thesis. The contributions concerning free-discontinuity problems for directly measured data in a linear space are the topic of Chapter 2.2. We deal with free-discontinuity problems in connection with inverse problems in Chapter 2.3. Then, we consider variational methods for manifold-valued data. The topic of Chapter 2.4 are free-discontinuity problems for manifold-valued data. In chapter 2.5, we consider total variation minimization for manifold-valued data as well as higher order generalizations.
Citations: Habilitationsschrift Universität Osnabrück, Fachbereich 6 - Mathematik/Informatik, Osnabrück, 2018
Subject Keywords: Mumford-Shah Modelle; Potts Modelle; TV Modelle; Variationelle Methoden; Algorithmen; Regularisierung; Entrauschen; Rekonstruktion; Bildverarbeitung; Bildgebung; Mannigfaltigkeitswertige Daten
Issue Date: 9-Jan-2020
License name: Attribution 3.0 Germany
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Type of publication: Buch [book]
Appears in Collections:FB06 - Hochschulschriften

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