Tue, 21 July, 2009, 14:00-15:00, C1
The topic of this talk are inverse problems with random data which are described
by a Poisson process, or after binning by a finite number of Poisson distributed
scalar random variables. Examples include deconvolution problems in fluorescence
microscopy, astronomy, and mass spectroscopy, SPECT, PET as well as phase
retrieval and inverse scattering problems in optics and quantum mechanics.
We study variational regularization methods in Banach spaces with the Kullback-Leibler
divergence as natural data misfit functional. Convergence and convergence rate
results are derived as the expected total number of counts (often proportional to
an illumination time) tends to infinity.
We conclude our talk with some real data examples from 4Pi fluorescence microscopy
and x-ray optics.
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