An accurate formula for the reconstruction of conductivity inhomogeneities |
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Authors: | Habib Ammari Jin Keun Seo |
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Affiliation: | a Centre de Mathématiques Appliquées, CNRS UMR 7641 & École Polytechnique, 91128, Palaiseau cedex, France;b Department of Mathematics, Yonsei University, Seoul 120-749, South Korea |
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Abstract: | We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy. |
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