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Bredies, K.* ; Holler, M.* ; Storath, M.* ; Weinmann, A.

Total generalized variation for manifold-valued data.

SIAM J. Imaging Sci. 11, 1785-1848 (2018)
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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
Quellenangaben Volume: 11, Issue: 3, Pages: 1785-1848 Article Number: , Supplement: ,
Publisher SIAM
Publishing Place Philadelphia, Pa.
Reviewing status