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SUMMARY:Multiscale Bounded Variation Regularization - Miguel del alamo (Ge
 org-August-Universität Göttingen)
DTSTART:20180323T100000Z
DTEND:20180323T110000Z
UID:TALK102808@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Housen Li (University of Goettingen)\, Axel 
 Munk (University of Goettingen)<br><br></span><span>In nonparametric regre
 ssion and inverse problems\, variational methods based on bounded variatio
 n (BV) penalties are a well-known and established tool for yielding edge-p
 reserving reconstructions\, which is a desirable feature in many applicati
 ons. Despite its practical success\, the theory behind BV-regularization i
 s poorly understood: most importantly\, there is a lack of convergence gua
 rantees in spatial dimension&nbsp\;d\\geq 2.<br><br></span>In this talk we
  present a variational estimator that combines a BV penalty and a multisca
 le constraint\, and prove that it converges to the truth at the optimal ra
 te. Our theoretical analysis relies on a proper analysis of the multiscale
  constraint\, which is motivated by the statistical properties of the nois
 e\, and relates in a natural way to certain Besov spaces of negative smoot
 hness. Further\, the main novelty of our approach is the use of refined in
 terpolation inequalities between function spaces. We also illustrate the p
 erformance of these variational estimators in simulations on signals and i
 mages.<br>
LOCATION:Seminar Room 1\, Newton Institute
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