Total Generalized Variation for Manifold-valued Data

TL;DR

This paper extends the concept of total generalized variation (TGV) regularization to manifold-valued data, providing a formal axiomatic framework, concrete instances, algorithms, and demonstrating its effectiveness through experiments.

Contribution

It introduces the first axiomatic approach to second-order TGV for manifold data, along with practical algorithms and experimental validation.

Findings

Well-posedness of the proposed TGV generalizations

Effective algorithms for manifold data

Successful application to synthetic and real data

Abstract

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.