Dr. Ronny Bergmann (TU Kaiserslautern): A Graph Framework for Manifold-valued Data
am Mittwoch, 26.07.2017 14:15 im Raum M4
In many real-world applications measured data are not in a Euclidean vector space but rather are given on a Riemannian manifold. This is the case, e.g., when dealing with Interferometric Synthetic Aperture Radar (InSAR) data consisting of phase values or data obtained in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI).
In this talk we present a framework for processing discrete manifold-valued data, for which the underlying (sampling) topology is modeled by a graph. We introduce the notion of a manifold-valued differences on a graph and based on this deduce a family of manifold-valued graph operators. In particular, we introduce the graph p-Laplacian and graph infinity-Laplacian for manifold-valued data. We discuss a numerical scheme to compute a solution to the corresponding parabolic PDEs and apply this algorithm to different manifold-valued data, illustrating the diversity and flexibility of the proposed framework in denoising and inpainting applications.
This is joint work with Daniel Tenbrinck (WWU Münster)