Variational Regularization of Inverse Problems for Manifold-Valued Data

TL;DR

This paper develops variational regularization methods, including TV and TGV, for inverse problems involving manifold-valued data, providing theoretical analysis, algorithms, and experimental validation.

Contribution

It introduces well-posedness results and algorithms for TV and TGV regularization of manifold-valued inverse problems, expanding existing methods to manifold data.

Findings

Algorithms successfully implement TV and TGV regularization on manifold data

Experimental results demonstrate effectiveness on synthetic and real data

Proposed methods show potential for practical applications in inverse problems

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.