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SUMMARY:Graph Methods for Manifold-valued Data - Daniel Tenbrinck (Univers
 ität Münster)
DTSTART:20171020T090000Z
DTEND:20171020T100000Z
UID:TALK89491@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Next to traditional processing tasks there exist real applicat
 ions in which measured data are not in a Euclidean vector space but rather
  are given on a Riemannian manifold. This is the case\, e.g.\, when dealin
 g with Interferometric Synthetic Aperture Radar (InSAR) data consisting of
  phase values or data obtained in Diffusion Tensor Magnetic Resonance Imag
 ing (DT-MRI).  In this talk we present a framework for processing discrete
  manifold-valued data\, for which the underlying (sampling) topology is mo
 deled by a graph. We introduce the notion of a manifold-valued derivative 
 on a graph and based on this deduce a family of manifold-valued graph oper
 ators. In particular\, we introduce the graph p-Laplacian and graph infini
 ty-Laplacian for manifold-valued data. We discuss a simple numerical schem
 e 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 appl
 ications.  This is joint work with Dr. Ronny Bergmann (TU Kaiserslautern).
LOCATION:Seminar Room 2\, Newton Institute
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