BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Analysis and applications of structural-prior-based total variatio
 n regularization for inverse problems - Martin Holler (University of Graz)
DTSTART:20171103T095000Z
DTEND:20171103T104000Z
UID:TALK94423@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Structural priors and joint regularization techniques\, such a
 s parallel level set methods and joint total variation\, have become quite
  popular recently in the context of variational image processing. Their ma
 in application scenario are particular settings in multi-modality/multi-sp
 ectral imaging\, where there is an expected correlation between different 
 channels of the image data. In this context\, one can distinguish between 
 two different approaches for exploiting such correlations: Joint reconstru
 ction techniques that tread all available channels equally and structural 
 prior techniques that assume some ground truth structural information to b
 e available. This talk focuses on a particular instance of the second type
  of methods\, namely structural total-variation-type functionals\, i.e.\, 
 functionals which integrate a spatially-dependent pointwise function of th
 e image gradient for regularization. While this type of methods has been s
 hown to work well in practical applications\, some of their analytical pro
 perties are not immediate. Those include a proper definition for BV functi
 ons and non-smooth a-priory data as well as existence results and regulari
 zation properties for standard inverse problem settings.   In this talk we
  address some of these issues and show how they can partially be overcome 
 using duality. Employing the framework of functions of a measure\, we defi
 ne structural-TV-type functionals via lower-semi-continuous relaxation. Si
 nce the relaxed functionals are\, in general\, not explicitly available\, 
 we show that instead of the classical Tikhonov regularization problem\, on
 e can equivalently solve a saddle-point problem where no a priori knowledg
 e of the relaxation is needed. In particular\, motivated by concrete appli
 cations\, we deduce corresponding results for linear inverse problems with
  norm and Poisson log-likelihood data discrepancy terms. The talk conclude
 s with proof-of-concept numerical examples.  This is joint work with M. Hi
 nterm&uuml\;ller and K. Papafitsoros (both from the Weierstrass Institute 
 Berlin)
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR