Associate Team ISIP

Problèmes de diffraction inverse et d'identification
(Inverse Scattering and Identification Problems)

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
 
 
French Coordinator
Partner Coordinator étranger
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

Team Members
David Colton (UDel)
Peter Monk (Udel)

Brief Description of the Research theme

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.


Proposal initial document


Evaluation report 2008-2010


Activity report 2011

Activity Report for 2012

Exchanges and stays of researchers and students between partners

Advancement of the work program (2012)

The associate team has made progress in the following directions

Joint papers produced in the realm of the associate team

  1. The Computation of Lower Bounds for the Norm of the Index of Refraction, J. Integral Equations and Applications, 21 203-227 (2009).
    Authors: F. Cakoni, H. Haddar, D. Colton.
  2. On the Determination of Dirichlet or Transmission Eigenvalues from Far Field Data, Comptes Rendus Mathematique, 348, No 7-8, 379-383 (2010).
    Authors: F. Cakoni, H. Haddar, D. Colton.
  3. On the existence of transmission eigenvalues in an inhomogenous medium, Applicable Analysis, 88 no 4, 475-493 (2009).
    Authors: F. Cakoni, H. Haddar
  4. The Interior Transmission Problem For regions with Cavities, SIAM Journal of Mathematical Analysis , 42, No 1, 145-162 (2010).
    Authors: F. Cakoni, H. Haddar, D. Colton.
  5. The existence of an infinite discrete set of transmission eigenvalues, SIAM Journal of Mathematical Analysis, 42, No 1, 237-255 (2010).
    Authors: F. Cakoni, D. Gintides, H. Haddar.
  6. A sampling method for inverse scattering in the time domain, Inverse Problems, 26, 8, paper 085001 (2010).
    Authors: Q. Chen, H. Haddar, A. Lechleiter and P. Monk,
  7. The interior transmission eigenvalue problem for absorbing media, Inverse Problems , 28, paper 045005 (2012).
    Authors:F. Cakoni, D. Colton, H. Haddar
  8. The interior transmission problem for inhomogeneous media containing perfect conductors, Inverse Problems and Imaging, Vol. 6, no. 3, (2012).
    Authors:F. Cakoni, A. Cossonnière, H. Haddar
  9. Transmission Eigenvalues in Inverse Scattering Theory, Chapter of the book Inside Out II, G. Uhlman Edition, (2012).
    Authors:F. Cakoni, H. Haddar
  10. The asymptotic of transmission eigenvalues for thin coatings, In preparation (2012).
    Authors:F. Cakoni, N. Chaulet, H. Haddar
  11. Surface integral equation for the electromagnetic interior transmission problem , In preparation (2012).
    Authors:F. Cakoni, H. Haddar

Workshops and scientific events organized in the realm of the associate team

Ongoing or completed PhD thesis co-supervised by the partners