Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
- 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.
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| Author: | Bastian von HarrachORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-716613 |
| DOI: | https://doi.org/10.1088/1361-6420/aaf6fc |
| ISSN: | 0266-5611 |
| Parent Title (English): | Inverse problems |
| Publisher: | Institute of Physics |
| Place of publication: | Bristol [u.a.] |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2019/01/03 |
| Date of first Publication: | 2019/01/03 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/01/26 |
| Volume: | 35 |
| Issue: | 024005 |
| Page Number: | 19 |
| HeBIS-PPN: | 507153960 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
