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Identification of small inhomogeneities: Asymptotic factorization
Author(s):
Habib
Ammari;
Roland
Griesmaier;
Martin
Hanke.
Journal:
Math. Comp.
76
(2007),
1425-1448.
MSC (2000):
Primary 35R30, 35C20
Posted:
February 19, 2007
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Abstract:
We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral equation methods. It demonstrates the strong relation between factorization methods and MUSIC-type methods for the solution of this inverse problem.
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Additional Information:
Habib
Ammari
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email:
ammari@cmapx.polytechnique.fr
Roland
Griesmaier
Affiliation:
Institut für Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany
Email:
griesmaier@math.uni-mainz.de
Martin
Hanke
Affiliation:
Institut für Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany
Email:
hanke@math.uni-mainz.de
DOI:
10.1090/S0025-5718-07-01946-1
PII:
S 0025-5718(07)01946-1
Keywords:
Electrical impedance tomography,
small conductivity inhomogeneities,
asymptotic expansions
Received by editor(s):
January 7, 2006
Received by editor(s) in revised form:
May 15, 2006.
Posted:
February 19, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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