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SUMMARY:Functions of bounded variation and derivative-based regularisation
 . Short Course: Higher order regularisation in imaging - Lecture 1 - Marti
 n Holler\, University of Graz
DTSTART:20171116T140000Z
DTEND:20171116T160000Z
UID:TALK94300@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:With growing computational resources on the one hand\, and dat
 a acquisition strategies approaching physical limits on the other hand\, m
 athematical methods are nowadays indispensable for achieving state of the 
 art results for concrete applications in image processing. There\, image r
 econstruction typically amounts to solve ill-posed operator equations\, an
 d variational methods and regularisation are crucial to obtain stable and 
 hence numerically feasible solution schemes.\n\nWhen dealing with image da
 ta\, regularisation\, besides allowing for stability\, also aims to incorp
 orate expected structures of the image-representing functions one aims to 
 recover.\nProminent examples of such structures are jump discontinuities\,
  corresponding to sharp edges\, and smooth regions.\nWhile the former can 
 be modelled well with the popular total variation functional\, which penal
 ises the Radon norm of the first order distributional derivative\, the lat
 ter requires to incorporate higher order differentiation. In that respect\
 , a main difficulty is to do this in a way such that jump discontinuities 
 can still be recovered.\n\nAddressing this challenge\, this course will co
 ver analytical aspects and concrete applications of higher order regularis
 ation approaches in imaging. Starting from the total variation functional\
 , we will consider different extensions from the perspective of modelling 
 image data and achieving a regularisation effect in ill-posed problems. Af
 ter establishing the fundamental theory\, we will also deal with a numeric
 al realisation and different applications in medical imaging and other dis
 ciplines.\n
LOCATION:MR4
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