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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Analysis and applications of structural-prior-base
d total variation regularization for inverse probl
ems - Martin Holler (University of Graz)
DTSTART;TZID=Europe/London:20171103T095000
DTEND;TZID=Europe/London:20171103T104000
UID:TALK94423AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/94423
DESCRIPTION:Structural priors and joint regularization techniq
ues\, such as parallel level set methods and joint
total variation\, have become quite popular recen
tly in the context of variational image processing
. Their main application scenario are particular s
ettings in multi-modality/multi-spectral imaging\,
where there is an expected correlation between di
fferent channels of the image data. In this contex
t\, one can distinguish between two different appr
oaches for exploiting such correlations: Joint rec
onstruction techniques that tread all available ch
annels equally and structural prior techniques tha
t assume some ground truth structural information
to be available. This talk focuses on a particular
instance of the second type of methods\, namely s
tructural total-variation-type functionals\, i.e.\
, functionals which integrate a spatially-dependen
t pointwise function of the image gradient for reg
ularization. While this type of methods has been s
hown to work well in practical applications\, some
of their analytical properties are not immediate.
Those include a proper definition for BV function
s and non-smooth a-priory data as well as existenc
e results and regularization properties for standa
rd inverse problem settings. In this talk we add
ress some of these issues and show how they can pa
rtially be overcome using duality. Employing the f
ramework of functions of a measure\, we define str
uctural-TV-type functionals via lower-semi-continu
ous relaxation. Since the relaxed functionals are\
, in general\, not explicitly available\, we show
that instead of the classical Tikhonov regularizat
ion problem\, one can equivalently solve a saddle-
point problem where no a priori knowledge of the r
elaxation is needed. In particular\, motivated by
concrete applications\, we deduce corresponding re
sults for linear inverse problems with norm and Po
isson log-likelihood data discrepancy terms. The t
alk concludes with proof-of-concept numerical exam
ples. This is joint work with M. Hintermü\;ll
er and K. Papafitsoros (both from the Weierstrass
Institute Berlin)
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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