Bregman distances in frequentist inverse problems

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.

• Speaker: Tapio Helin, University of Helsinki
• Wednesday 31 January 2018, 14:00–15:00
• Venue: MR3 Centre for Mathematical Sciences.
• Series: CCIMI Seminars; organiser: Rachel Furner.