Total Generalized Variation for Manifold-valued Data
This work extends TGV regularization to manifold-valued data, addressing a gap for applications like diffusion tensor imaging or directional statistics, but the contribution is incremental as it adapts existing concepts.
The paper introduces second-order total generalized variation (TGV) regularization for manifold-valued data, providing two concrete instances that fulfill proposed axioms, with well-posedness results and numerical algorithms. Experiments on synthetic and real data demonstrate the potential for applications.
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.