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SUMMARY:Total Generalized Variation for Manifold-valued Data - Martin Holl
 er (University of Graz)
DTSTART:20170908T135000Z
DTEND:20170908T144000Z
UID:TALK78501@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Kristian Bredies		(University of Graz)\, Mar
 tin Storath		(University of Heidelberg)\, Andreas Weinmann		(Darmstadt Uni
 versity of Applied Sciences)        <br></span><span><br>Introduced in 201
 0\, the total generalized variation (TGV) functional is nowadays amongst t
 he most successful regularization functionals for variational image recons
 truction. It is defined for an arbitrary order of differentiation and prov
 ides a convex model for piecewise smooth vector-space data. On the other h
 and\, variational models for manifold-valued data have become popular rece
 ntly and many successful approaches\, such as first- and second-order TV r
 egularization\, have been successfully generalized to this setting. Despit
 e the fact that TGV regularization is\, generally\, considered to be prefe
 rable to such approaches\, an appropriate extension for manifold-valued da
 ta was still missing. In this talk we introduce the notion of second-order
  total generalized variation (TGV) regularization for manifold-valued data
 . We provide an axiomatic approach to formalize reasonable generalizations
  of TGV to the manifold setting and present concrete instances that fulfil
 l the proposed axioms. We prove well-posedness results and present algorit
 hms for a numerical realization of these generalizations to the manifold s
 etup. Further\, we provide experimental results for synthetic and real dat
 a to further underpin the proposed generalization numerically and show its
  potential for applications with manifold-valued data.</span>
LOCATION:Seminar Room 1\, Newton Institute
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