Variational regularization of inverse problems for manifold-valued data. (16th June 2020)

• Record Type: Journal Article
• Authors: Storath, Martin; Weinmann, Andreas
• Is Part Of: Information and inference. Volume 10:Number 1(2021)
• Page Start: 195
• Page End: 230
• Publication Date: 2020-06-16
• Subjects: manifold-valued data -- inverse problems -- indirect measurement operator -- TV regularization -- higher-order regularization; Mathematical models -- Periodicals; 519.605
• DOI: 10.1093/imaiai/iaaa010
• Languages: English
• ISSNs: 2049-8764

Abstract

Abstract: In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider total variation and total generalized variation 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.