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CATEGORIES:Cambridge Image Analysis Seminars
SUMMARY:Inverse Scale Space Decomposition - Marie Foged Sc
hmidt\, Denmark Technical University (DTU)
DTSTART;TZID=Europe/London:20160916T160000
DTEND;TZID=Europe/London:20160916T170000
UID:TALK67496AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67496
DESCRIPTION:In this talk we study the behaviour of the inverse
scale space flow for computing an approximate sol
ution to an inverse problem. The flow is a time-co
ntinuous version of Bregman iteration and has show
n superior properties to standard regularization m
ethods. The flow starts in the null space of the r
egularization functional and then incorporates fin
er and finer scales depending on the regularizatio
n. We want to study the inverse scale space flow f
or a specific structure of the measured data for l
inear inverse problems. To define the considered s
tructure of the data we introduce what is called g
eneralized singular vectors.\n \nGeneralized singu
lar vectors arise from a generalization of the con
cept of singular vectors of linear operators to va
riational frameworks. The generalized singular vec
tors define a new concept of scale depending on th
e regularization functional. We show that the inv
erse scale space flow gives a decomposition into g
eneralized singular vectors under certain conditio
ns when the regularization functional is absolutel
y one-homogeneous and the data for the inverse pro
blem is given as the forward operator applied to a
linear combination of the singular vectors.\n \nF
inally\, we address and discuss the question about
when the first non-trivial solution of the invers
e scale space flow is a generalized singular vecto
r. At this point we define what we will call dual
singular vectors which may actually be a better st
arting point for the structure of the data than ge
neralized singular vectors.
LOCATION:MR 14\, Centre for Mathematical Sciences
CONTACT:Martin Benning
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