TY  - JOUR
A1  - Harrach, Bastian von
T1  - Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
T2  - Inverse problems
N2  - For the linearized reconstruction problem in electrical impedance tomography with the complete electrode model, Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a fixed partition is uniquely determined if enough electrodes are being used. We extend their result to the full non-linear case and show that measurements on a sufficiently high number of electrodes uniquely determine a conductivity in any finite-dimensional subset of piecewise-analytic functions. We also prove Lipschitz stability, and derive analogue results for the continuum model, where finitely many measurements determine a finite-dimensional Galerkin projection of the Neumann-to-Dirichlet operator on a boundary part.
Y1  - 2019
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/71661
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-716613
SN  - 0266-5611
VL  - 35
IS  - 024005
PB  - Institute of Physics
CY  - Bristol [u.a.]
ER  -