Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-313| Authors: | Gebauer, Bastian Hyvönen, Nuutti |
| Title: | Factorization method and irregular inclusions in electrical impedance tomography |
| Online publication date: | 19-Nov-2008 |
| Year of first publication: | 2007 |
| Language: | english |
| Abstract: | In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments. |
| DDC: | 510 Mathematik 510 Mathematics |
| Institution: | Johannes Gutenberg-Universität Mainz |
| Department: | FB 08 Physik, Mathematik u. Informatik |
| Place: | Mainz |
| ROR: | https://ror.org/023b0x485 |
| DOI: | http://doi.org/10.25358/openscience-313 |
| URN: | urn:nbn:de:hebis:77-17968 |
| Version: | Published version |
| Publication type: | Zeitschriftenaufsatz |
| License: | In Copyright |
| Information on rights of use: | https://rightsstatements.org/vocab/InC/1.0/ |
| Journal: | Inverse problems 23 |
| Pages or article number: | 2159 2170 |
| Publisher place: | Bristol u.a. |
| Issue date: | 2007 |
| ISSN: | 1361-6420 0266-5611 |
| Appears in collections: | JGU-Publikationen |
