Total generalized variation for manifold-valued data
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 t...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
05 July 2018
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| In: |
SIAM journal on imaging sciences
Year: 2018, Volume: 11, Issue: 3, Pages: 1785-1848 |
| ISSN: | 1936-4954 |
| DOI: | 10.1137/17M1147597 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1137/17M1147597 Verlag, Volltext: https://epubs.siam.org/doi/10.1137/17M1147597 
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| Author Notes: | K. Bredies, M. Holler, M. Storath, and A. Weinmann |
| Summary: | 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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| Item Description: | Gesehen am 06.08.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1936-4954 |
| DOI: | 10.1137/17M1147597 |