Associate Team ISIP
| INRIA project-team : DeFI | Partner : Department of Mathematical Sciences University of Delaware |
| Centre de recherche INRIA : INRIA Saclay Ile de
France Thème INRIA : NumD |
Pays : France |
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French Coordinator
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Partner Coordinator
étranger
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| Nom, prénom | HADDAR Houssem | CAKONI Fioralba |
| Grade/statut | DR2 (Habilitation) | Professor |
| Organisme d'appartenance |
Equipe DeFI (INRIA Saclay Ile de France/Ecole Polytechnique) | Department of Mathematical Sciences, University of Delaware |
| Adresse postale | CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex France | Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553 USA |
| URL | http://www-rocq.inria.fr/~haddar/ | http://www.math.udel.edu/~cakoni/ |
| Téléphone | +33 1 69 33 46 41 | +1 302 831 0592 |
| Télécopie | +33 1 69 33 30 11 | +1 302 831 4511 |
| Courriel | Housem.Haddar@inria.fr | cakoni@math.udel.edu |
|
David Colton (UDel) Armin Lechleiter (DeFI) Peter Monk (Udel) |
The associated team will concentrate on the use of qualitative methods in electromagnetic inverse scattering theory with applications to the imaging of urban infrastructure, the nondestructive evaluation of coated materials and medical imaging. Most of the effort will be focused in the solution of the inverse problems using time harmonic waves, in particular for frequencies in the resonance regime. The aim of research in this field is to not only detect but also to identify unknown objects in real time. Mathematically, such problems lead to nonlinear and severely ill-posed equations. Until a few years ago, essentially all existing algorithms for target identification were based on either a weak scattering approximation or on the use of nonlinear optimization techniques. In recent years alternative methods for imaging, known as qualitative methods, have been developed which avoid incorrect model assumptions inherent in weak scattering approximations and, as opposed to nonlinear optimization techniques, do not require a priori information. In addition, these methods are non iterative and are based on finding an indicator function which is usually a solution of a linear ill-posed integral equation. This leads to an easily implementable and fast imaging technique. The best known qualitative method is the linear sampling method and it's close relative the reciprocitygap functional method. We will use the linear sampling method and the reciprocity gap functional method to investigate a number of complex imagining problems in the areas listed above in which there is practically no a priori information on the geometry and physical properties of the scatterer and the aim is to reconstruct the shape and/or estimate the constitutive physical parameters of the object. |