Total generalized variation for manifold-valued data

• Verfasst von: Bredies, Kristian [VerfasserIn]
• Verfasst von: Storath, Martin [VerfasserIn]
• Titel: Total generalized variation for manifold-valued data
• Verf.angabe: K. Bredies, M. Holler, M. Storath, and A. Weinmann
• E-Jahr: 2018
• Jahr: 05 July 2018
• Umfang: 64 S.
• Fussnoten: Gesehen am 06.08.2019
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on imaging sciences
• Ort Quelle: Philadelphia, Pa. : SIAM, 2008
• Jahr Quelle: 2018
• Band/Heft Quelle: 11(2018), 3, Seite 1785-1848
• ISSN Quelle: 1936-4954
• DOI: doi:10.1137/17M1147597
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1670661423

Abstract

In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data in a discrete setting. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for synthetic and real data to further underpin the proposed generalization numerically and show its potential for applications with manifold-valued data.