On imaging obstacles inside inhomogeneous media |
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Authors: | Adrian I Nachman Ari Teirilä |
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Institution: | a Department of Mathematics and Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada b Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland c Kajaani Polytechnic, Kajaani, Finland |
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Abstract: | We show that an obstacle inside a known inhomogeneous medium can be determined from measurements of the scattering amplitude at one frequency, without a priori knowledge of the boundary condition. We also show that an obstacle inside a known inhomogeneous anisotropic conducting medium can be determined from electrostatic current and voltage measurements on the boundary of a domain containing the obstacle. Moreover, two obstacles with boundary measurements which are merely comparable as operators must be identical. The first part of the paper gives an extension of the factorization method which may be of independent interest and also yields a new reconstruction procedure. |
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Keywords: | Imaging Obstacles Inhomogeneous media Inverse scattering Electrical tomography Factorization method |
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