The total generalized variation (TGV) functional provides a convex model for piecewise smooth vector-space data and is amongst the most successful regularization functionals for variational image reconstruction. In this talk, we introduce the notion of second-order TGV regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to this setting and present concrete instances that fulfill the proposed axioms. We prove well-posedness results and present numerical algorithms and experimental results.

This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .

Authors:

Kristian Bredies (Universität Graz)

Martin Holler (École Polytechnique, Université Paris Saclay)

Andreas Weinmann (Hochschule Darmstadt)

Martin Storath (Universität Heidelberg)

Keywords:

image reconstruction, manifold-valued data, total generalized variation