Regularization of Inverse Problems with Large Noise

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• Thorsten Hohage (Georg August Universität Göttingen)
• Thursday 08 May 2014, 15:00-16:00
• MR 14, CMS.

If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

We consider ill-posed inverse problems described by operator equations F(x)=y in Banach spaces. The focus of this talk is on observations of y which are perturbed by ’’large’’ noise in the sense that they do not belong to the same Banach space as y. One may argue that this is the case for all real data as practical observations are always finite dimensional, but in many standard statistical noise models such of white noise processes and Poisson data even the infinite dimensional limits belong to a different space. We derive results on convergence and rates of convergence in expectation for Poisson data and for impulsive noise. These result are illustrated for phase retrieval problems in coherent x-ray imaging, inverse scattering problems, and parameter identification problems in stochastic differential equations.

This talk is part of the Applied and Computational Analysis series.

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