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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multiscale Bounded Variation Regularization - Migu
el del alamo (Georg-August-Universität Göttingen)
DTSTART;TZID=Europe/London:20180323T100000
DTEND;TZID=Europe/London:20180323T110000
UID:TALK102805AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102805
DESCRIPTION:Co-authors: Housen Li (University of Goettin
gen)\, Axel Munk (University of Goettingen)
In nonparametric regression and inve
rse problems\, variational methods based on bounde
d variation (BV) penalties are a well-known and es
tablished tool for yielding edge-preserving recons
tructions\, which is a desirable feature in many a
pplications. Despite its practical success\, the t
heory behind BV-regularization is poorly understoo
d: most importantly\, there is a lack of convergen
ce guarantees in spatial dimension \;d\\geq 2.
In this talk we present a variation
al estimator that combines a BV penalty and a mult
iscale constraint\, and prove that it converges to
the truth at the optimal rate. Our theoretical an
alysis relies on a proper analysis of the multisca
le constraint\, which is motivated by the statisti
cal properties of the noise\, and relates in a nat
ural way to certain Besov spaces of negative smoot
hness. Further\, the main novelty of our approach
is the use of refined interpolation inequalities b
etween function spaces. We also illustrate the per
formance of these variational estimators in simula
tions on signals and images.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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