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Bregman distances in frequentist inverse problems

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We consider variational regularisation methods for inverse problems with Gaussian random white noise. We derive frequentist consistency results for linear inverse problems with p-homogeneous regularisation functionals in terms of the expectation of a symmetric Bregman distance. A key observation, which guides us through the analysis, is that the random noise can be analysed with techniques from regularisation literature relating to approximate source conditions. This is joint work with Martin Burger and Hanne Kekkonen.

This talk is part of the CCIMI Seminars series.

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