22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

A model reduction approach for inverse problems with operator valued data

24 Sep 2021, 10:50
30m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Matthias Schlottbom (University of Twente)

Description

We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies extremely high computational cost already for the evaluation of the forward operator, which makes a numerical solution of the inverse problem, e.g., by iterative regularization methods, practically infeasible. To overcome this obstacle, we develop a novel model reduction approach that takes advantage of the underlying tensor product structure of the problem and which allows to obtain low-dimensional certified reduced order models of quasi-optimal rank. The theoretical results are illustrated by application to a typical model problem in fluorescence optical tomography.

Primary authors

Prof. Herbert Egger (JKU Linz) Prof. Jürgen Dölz (University of Bonn) Matthias Schlottbom (University of Twente)

Presentation Materials

There are no materials yet.