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Ruprecht-Karls-Universität Heidelberg Institute of Applied Mathematics Statistics of inverse problems Research Group
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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Bachelor in Mathematics

Author:
Merlin Dietrich

Title:
Deconvolution with an unknown kernel in a Bayesian perspective

Supervisor:
Jan JOHANNES

Abstract:
The aim of this thesis is to introduce the inverse problem of deconvolution with uncertainty in the operator in a Bayesian statistical setting. I will give a comprehensive formal introduction into Bayesian statistical modeling and keep the framework of the deconvolution as simple as possible, while still mapping the complexity of statistical inverse problems with unknown operators. I then present an approach of solving this inverse problem, that is entirely data driven, yet Bayesian. This ’solution’ will be justified in a rather frequentist analysis, by proving that it asymptotically concentrates around a postulated ’truth’. The idea of the data driven Bayesian ’solution’ and its analysis closely follow the lines of Trabs (2018) in his work on Bayesian inverse problems with unknown operators.

References:
M. Trabs. Bayesian inverse problems with unknown operators. Inverse Problems, 34(8):085001, 27, 2018.