Variational Regularization of Inverse Problems for Manifold-Valued Data

2018/04/27 by Storath, Martin, Weinmann, Andreas
#53B99 #65K10 #68U10 #90C90 #94A08 #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1804.10432

Abstract

In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide results on the well-posedness and present algorithms for a numerical realization of these models in the manifold setup. Further, we provide experimental results for synthetic and real data to show the potential of the proposed schemes for applications.

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