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Total generalized variation for manifold-valued data.
SIAM J. Imaging Sci. 11, 1785-1848 (2018)
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.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Denoising ; Higher Order Regularization ; Manifold-valued Data ; Total Generalized Variation; Total Variation Regularization; Proximal Point Algorithm; Extrinsic Sample Means; Tgv-based Framework; Riemannian-manifolds; Image Decompression; Bounded Variation; Corpus-callosum; Diffusion; Spaces
ISSN (print) / ISBN
1936-4954
Journal
SIAM Journal on Imaging Sciences
Quellenangaben
Volume: 11,
Issue: 3,
Pages: 1785-1848
Publisher
SIAM
Publishing Place
Philadelphia, Pa.
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)