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

The tangential cone condition for EIT

22 Sep 2021, 10:20
30m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Stefan Kindermann (Johannes Kepler University Linz)

Description

The tangential cone conditions (TCCs) are sufficient conditions on a nonlinear forward operator for proving convergence of various iterative nonlinear regularization schemes such as Landweber iteration. Especially for parameter identification problems with boundary data, they have not been verified yet, even though numerical results for nonlinear iterative regularization method
usually show the expected convergence behavior. In this talk we analyze the tangential cone conditions for the classical impedance tomography problem (EIT) and state sufficient conditions when they hold, although a general result on the validity of the TCCs remains open. An important tool is the use of Loewner monotonicity, which allows us to prove the TCC in situations, e.g., when the conductivities are pointwisely above or below the true conductivity. This talk is a summary of the arXiv article [1]

[1] S. Kindermann, On the tangential cone condition for electrical impedance tomography,
Preprint on arXiv, 2021. https://arxiv.org/abs/2105.02635

Primary author

Stefan Kindermann (Johannes Kepler University Linz)

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