Total Generalized Variation for Manifold-valued Data
University of Graz（格拉茨大学）；Heidelberg Collaboratory for Image Processing, Universität Heidelberg（海德堡大学图像分析协作中心）；Institute of Computational Biology, Helmholtz Zentrum München（慕尼黑亥姆霍兹中心计算生物学研究所）；Department of Mathematics and Natural Sciences, Hochschule Darmstadt（达姆施塔特应用技术大学数学与自然科学系）
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.
A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学促进学会数学研究所）；Technische Universität Kaiserslautern（凯泽斯劳滕工业大学）；Technische Universität München（慕尼黑工业大学）；Helmholtz-Zentrum München（赫尔姆霍兹慕尼黑中心）
Variational Regularization of Inverse Problems for Manifold-Valued Data
Image Analysis and Learning Group, Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Germany（图像分析与学习组，跨学科科学计算中心，海德堡大学，德国）；Department of Mathematics and Natural Sciences, Hochschule Darmstadt, and Institute of Computational Biology, Helmholtz Zentrum München, Germany（数学与自然科学系，达姆施塔特应用科学大学，以及计算生物学研究所，海德堡研究中心，德国）
