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SUMMARY:Regularization of Inverse Problems with Large Noise - Thorsten Hoh
 age (Georg August Universität Göttingen)
DTSTART:20140508T140000Z
DTEND:20140508T150000Z
UID:TALK50725@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:We consider ill-posed inverse problems described by operator e
 quations F(x)=y in Banach spaces. The focus of this talk is on observation
 s of y which are perturbed by ''large'' noise in the sense that they do no
 t belong to the same Banach space as y. \nOne may argue that this is the c
 ase for all real data as practical \nobservations are always finite dimens
 ional\, but in many standard \nstatistical noise models such of white nois
 e processes and Poisson \ndata even the infinite dimensional limits belong
  to a different space. \nWe derive results on convergence and rates of con
 vergence in expectation for Poisson data and for impulsive noise. \nThese 
 result are illustrated for phase retrieval problems in coherent \nx-ray im
 aging\, inverse scattering problems\, and parameter identification problem
 s in stochastic differential equations. 
LOCATION:MR 14\, CMS
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