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CATEGORIES:Cambridge Image Analysis Seminars
SUMMARY:Sparse solutions for dynamic inverse problems with
Optimal Transport regularisers - Marcello Carioni
\, University of Graz
DTSTART;TZID=Europe/London:20200122T130000
DTEND;TZID=Europe/London:20200122T140000
UID:TALK138553AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138553
DESCRIPTION:The aim of the first part of this talk is to provi
de a characterization for sparse solutions of abst
ract variational inverse problems with finite dime
nsional data. We consider the minimization of func
tionals that are the sum of two terms: a convex re
gularizer and a finite dimensional soft constraint
. It was observed for specific examples that minim
izers of variational problems of this type are spa
rse in a suitable sense. We formalise this fact pr
oving the existence of a minimizer that is represe
nted as a finite linear combination of extremal po
ints of the unit ball of the regularizer. This fin
ding provides a natural notion of sparsity for abs
tract variational inverse problems. \nWe apply thi
s abstract result to relevant examples as TV denoi
sing and higher order scalar regularizers. Then\,
we consider the framework of dynamic inverse probl
ems with the Benamou-Brenier energy as a regulariz
er. Using the classical theory of Optimal Transpor
t\, we provide a characterisation for sparse solut
ions in this specific case. Then\, in the last par
t of the talk\, we show how to construct a variant
of the Alternating Descent Conditional Gradient M
ethod that relies on the structure of sparse solut
ions for dynamic inverse problems.
LOCATION:MR 14\, Centre for Mathematical Sciences
CONTACT:Yury Korolev
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