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SUMMARY:Inverse Scale Space Decomposition - Marie Foged Schmidt\, Denmark 
 Technical University (DTU)
DTSTART:20160916T150000Z
DTEND:20160916T160000Z
UID:TALK67496@talks.cam.ac.uk
CONTACT:Martin Benning
DESCRIPTION:In this talk we study the behaviour of the inverse scale space
  flow for computing an approximate solution to an inverse problem. The flo
 w is a time-continuous version of Bregman iteration and has shown superior
  properties to standard regularization methods. The flow starts in the nul
 l space of the regularization functional and then incorporates finer and f
 iner scales depending on the regularization. We want to study the inverse 
 scale space flow for a specific structure of the measured data for linear 
 inverse problems. To define the considered structure of the data we introd
 uce what is called generalized singular vectors.\n \nGeneralized singular 
 vectors arise from a generalization of the concept of singular vectors of 
 linear operators to variational frameworks. The generalized singular vecto
 rs define a new concept of scale depending on the regularization functiona
 l. We  show that the inverse scale space flow gives a decomposition into g
 eneralized singular vectors under certain conditions when the regularizati
 on functional is absolutely one-homogeneous and the data for the inverse p
 roblem is given as the forward operator applied to a linear combination of
  the singular vectors.\n \nFinally\, we address and discuss the question a
 bout when the first non-trivial solution of the inverse scale space flow i
 s a generalized singular vector. At this point we define what we will call
  dual singular vectors which may actually be a better starting point for t
 he structure of the data than generalized singular vectors.
LOCATION:MR 14\, Centre for Mathematical Sciences
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