Variational Regularization of Inverse Problems for Manifold-Valued Data
This work addresses inverse problems for data on manifolds, which is incremental as it extends existing regularization methods to a more complex data structure.
The paper tackles the variational regularization of manifold-valued data in inverse problems by extending TV and TGV regularization to handle indirect measurements, providing well-posedness results and algorithms for numerical implementation.
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.