Identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements |
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Authors: | Habib Ammari |
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Affiliation: | Centre de Mathématiques Appliquées, CNRS UMR 7641 & École Polytechnique, 91128 Palaiseau cedex, France |
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Abstract: | We consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial (on part of the boundary) dynamic boundary measurements. Through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations. This asymptotic formula is generalized to the full time-dependent Maxwell's equations. Our formulae may be expected to lead to very effective computational identification algorithms, aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements. |
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Keywords: | Inverse problem Wave equation Maxwell's equations Reconstruction Electromagnetic coefficients Geometric control |
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