Multi-static response matrix of a 3-D inclusion in half space and MUSIC imaging

Ekaterina Iakovleva 1 Souhir Gdoura 2 Dominique Lesselier 2 Gaële Perrusson 2
1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 L2S - Laboratoire des signaux et systèmes
Abstract : Recent work on the retrieval of 3-D bounded di- electric and/or magnetic inclusions in free space is extended to burial in a half-space. Though emphasis is on the case of a single inclusion, enabling the derivation of closed-form mathematical results in illuminating fashion, the approach extends to the case of (an unknown number of) well-separated inclusions. Within an asymptotic field formulation derived from exact contrast-source vector integral formulations satisfied by the time-harmonic fields and using proper reciprocity relationships of the dyadic Green's functions, the multistatic response matrix of the inclusion is constructed from the leading-order term of the fields. Its singular value structure is analyzed in detail for a dielectric or a magnetic contrast, or both contrasts. This is performed in the case of a unique electric dipole array operated in the transmit/receive mode at a single frequency. A multiple signal classification-type algo- rithm follows from the decomposition, yielding a cost functional the magnitude of which peaks at the inclusion center. Numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration. Imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data, as well as of two inclusions embedded within a non-conductive or conductive half space.
Keywords : time-harmonic 3-D electromagnetic scattering Asymptotic formulation Green's dyadic function half-space MUltiple SIgnal Classification (MUSIC) multistatic response (MSR) time-harmonic 3-D electromagnetic scattering.
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Journal articles
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https://hal-supelec.archives-ouvertes.fr/hal-00270645
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Submitted on : Monday, April 7, 2008 - 10:49:53 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM

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Ekaterina Iakovleva, Souhir Gdoura, Dominique Lesselier, Gaële Perrusson. Multi-static response matrix of a 3-D inclusion in half space and MUSIC imaging. IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2007, 55 (9), pp.2598-2609. ⟨10.1109/TAP.2007.904103⟩. ⟨hal-00270645⟩

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