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Authors: Gebauer, Bastian
Hyvönen, Nuutti
Title: Factorization method and irregular inclusions in electrical impedance tomography
Online publication date: 19-Nov-2008
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
URN: urn:nbn:de:hebis:77-17968
Version: Published version
Publication type: Zeitschriftenaufsatz
License: In Copyright
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Journal: Inverse problems
Pages or article number: 2159
Publisher place: Bristol u.a.
Issue date: 2007
ISSN: 1361-6420
Appears in collections:JGU-Publikationen

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