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CATEGORIES:Short Course: Higher order regularisation in imagi
ng
SUMMARY:Functions of bounded variation and derivative-base
d regularisation. Short Course: Higher order regul
arisation in imaging - Lecture 1 - Martin Holler\,
University of Graz
DTSTART;TZID=Europe/London:20171116T140000
DTEND;TZID=Europe/London:20171116T160000
UID:TALK94300AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/94300
DESCRIPTION:With growing computational resources on the one ha
nd\, and data acquisition strategies approaching p
hysical limits on the other hand\, mathematical me
thods are nowadays indispensable for achieving sta
te of the art results for concrete applications in
image processing. There\, image reconstruction ty
pically amounts to solve ill-posed operator equati
ons\, and variational methods and regularisation a
re crucial to obtain stable and hence numerically
feasible solution schemes.\n\nWhen dealing with im
age data\, regularisation\, besides allowing for s
tability\, also aims to incorporate expected struc
tures of the image-representing functions one aims
to recover.\nProminent examples of such structure
s are jump discontinuities\, corresponding to shar
p edges\, and smooth regions.\nWhile the former ca
n be modelled well with the popular total variatio
n functional\, which penalises the Radon norm of t
he first order distributional derivative\, the lat
ter requires to incorporate higher order different
iation. In that respect\, a main difficulty is to
do this in a way such that jump discontinuities ca
n still be recovered.\n\nAddressing this challenge
\, this course will cover analytical aspects and c
oncrete applications of higher order regularisatio
n approaches in imaging. Starting from the total v
ariation functional\, we will consider different e
xtensions from the perspective of modelling image
data and achieving a regularisation effect in ill-
posed problems. After establishing the fundamental
theory\, we will also deal with a numerical reali
sation and different applications in medical imagi
ng and other disciplines.\n
LOCATION:MR4
CONTACT:Rachel Furner
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