Direction des
Relations Internationales (DRI)
Programme
INRIA "Equipes Associées"
(Demande de prolongation)
I. DEFINITION
EQUIPE ASSOCIEE
|
ISIP |
|
sélection
|
2008 |
| Equipe-Projet INRIA : DeFI |
Organisme étranger partenaire : Department
of Mathematical Sciences University of Delaware |
Centre de recherche INRIA : INRIA Saclay Ile de
France
Thème INRIA : NumD |
Pays : France |
| |
Coordinateur
français
|
Coordinateur
étranger
|
| Nom, prénom |
HADDAR Houssem |
CAKONI Fioralba |
| Grade/statut |
DR2 (Habilitation) |
Associate 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 |
La proposition en bref
|
Titre de la thématique de
collaboration (en français et en anglais)
:
Problèmes de diffraction inverse et
d'identification
(Inverse Scattering and Identification Problems)
|
Descriptif
:
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.
|
II. BILAN 2009
|
Changements majeurs survenus concernant
l'Equipe Associée (modifications des objectifs scientifiques,
des chercheurs impliqués)
A. Lechleiter, hired in 2009 as CR2 in the DEFI team, has joined the
associate team as a permanent member since September 2009.
|
Rapport scientifique de
l'année 2009
Description de l'activité scientifique de
l'équipe associée et des résultats obtenus :
publications, communications, organisation de colloques, formation,
soutenances de thèse, valorisation économique, sociale,
industrielle, enregistrement de logiciels, dépôt de
brevets ... (1 à 2 pages)
The Associated team has participated in 2009 to the international
scientific animation through several events:
Scientific production in 2009 (articles submitted in 2008 (see
scientific production of 2008) are accepted)
- Related to the conference "International Conference on Inverse
Scattering Problems" (web page of
the ICISP conference), honoring David Colton and Rainer Kress,
organized by F. Cakoni, H. Haddar and
M. Piana, the organizers edited a special issue of the journal Inverse Problems
and Imaging. The special issue (Volume 3, Number 2) appeared in
2009. The content of this issue is available at http://aimsciences.org/journals/displayPapers1.jsp?pubID=304
- On the Determination of Dirichlet or Transmission
Eigenvalues from Far Field Data (article submitted in 2009)
Authors F. Cakoni, H. Haddar, D. Colton.
Abstract: We show that the Herglotz wave function with
kernel the Tikhonov regularized
solution of the far field equation becomes unbounded as the
regularization
parameter tends to zero iff the wavenumber $k$ belongs to a discrete
set of values. When the scatterer is such that the total field vanishes
on the boundary, these values correspond to the square root of
Dirichlet eigenvalues for $-\Delta$. When the scatterer is a non
absorbing inhomogeneous medium these values correspond to so-called
transmission eigenvalues.
- The Interior Transmission Problem For regions with Cavities
(article submitted in 2009)
Authors F. Cakoni, H. Haddar, D. Colton.
Abstract: We consider the interior transmission problem in
the case when the inhomogeneous medium has cavities, i.e. regions in
which the index of refraction is the same as the host medium. In this
case we establish the Fredholm property for this problem and show that
transmission eigenvalues exist and form a discrete set. We also derive
Faber-Krahn type inequalities for the transmission eigenvalues.
- The existence of an infinite discrete set of transmission
eigenvalues (article submitted in 2009)
Authors F. Cakoni, D. Gintides, H. Haddar.
Abstract: We prove the existence of an infinite discrete
set of transmission eigenvalues corresponding to the scattering problem
for isotropic as well as anisotropic inhomogeneous media for the
Helmholtz and Maxwell's equations. Our discussion also includes the
case of the interior transmission problem for an inhomogeneous medium
with cavities, i.e. subregions with contrast zero.
- During a one month training of Q. Chen within the DEFI
team, we continued investigating the extension of the linear sampling
method to inverse scattering problems in the time domain. This theme is
now
pursuied together with A. Lechleiter and P. Monk. We validated the
methodology
in the case of small obstacles and the work is still in progress for
extended
obstacles.
- A. Cossonniere started a PhD studies in September 2008 on the use
of
transmission eigenvalues in inverse scattering problem for the 3D
electromagnetic
problem. The main goal of her thesis is to extend some of the resultas
obtained
by Cakoni-Haddar-Colton in the scalar case to the full Maxwell problem.
In this perspective, theoretcial results related to resolution of the
interior
transmission problem for medium with cavities and existence of
transmission
eigenvalues have been obtained. In the period September-December 2009,
A. Cossonniere is visiting UDEL and is working on the continuity of
transmission eigenvalues with respect to the medium properties.
Parallel to
this work, G. Giorgi, who started in 2009 a PhD thesis co-directed by
H. Haddar
and M. Piana begun investigating (during a three months training at the
DEFI
team) a new procedure to improve the lower bound
on medium index from observed transmission eigenvalue based on ideas
inspired
by the work of F. Cakoni, D. Gintides, H. Haddar mentioned above.
Rapport financier 2009
Avant de remplir les tableaux, consultez les
règles au paragraphe "Financement" de la page
d'accueil du programme.
| 1.
Dépenses EA (effectuées sur les crédits de
l'Equipe Associée) |
Montant dépensé
|
| Invitations des partenaires |
12577 |
| Missions INRIA |
5232 |
|
Total
|
17809 |
L'utilisation des credits et leur repartition se trouvent justifie dans le tableau (Bilan des echanges effectues en 2009) et le resume de la production scientifique en 2009.
| 2.
Dépenses externes (effectuées sur des financements
hors EA) |
Montant dépensé
|
| UDEL (*): |
| Invitations des partenaires |
7635 |
| Missions INRIA vers le partenaire |
2000 |
|
Total
|
9635 |
Total des financements externes dépensés
|
9635
|
Total des financements EA et externes dépensés
|
27444
|
Bilan des échanges
effectués en 2009
1. Chercheurs Seniors
|
Nom
|
statut (1)
|
provenance |
destination
|
objet (2)
|
durée (3)
|
Coût (si financement EA)
|
Coût (si financement externe)
|
| F. Cakoni |
Pr. |
UDEL |
INRIA |
visite |
1 semaine |
1509 |
|
| F. Cakoni |
Pr. |
UDEL |
INRIA+PAU |
visite+conf |
2 semaines |
2895 |
|
| F. Cakoni |
Pr. |
UDEL |
VIENNA |
conf. |
1 semaine |
|
2000
|
| D. Colton |
Pr. |
UDEL |
INRIA |
visite |
1 semaine |
1496 |
|
| S. Chaabane |
Pr. |
ENIT |
VIENNA |
conf |
1 semaine |
1373 |
|
| L. Bourgeois |
Pr. |
INRIA |
VIENNA |
conf |
1 semaine |
1270 |
|
| H. Haddar |
Dr. |
INRIA |
VIENNA |
conf |
1 semaine |
1270 |
|
(1) DR / CR / professeur
(2) colloque, thèse, stage,
visite....
(3) précisez l'unité (mois, semaine..)
2. Juniors
|
Nom
|
statut (1)
|
provenance
|
destination |
objet (2)
|
durée (3)
|
Coût (si financement EA)
|
Coût (si financement externe)
|
| R. Griesmaier |
PostDoc |
UDEL |
INRIA |
visite |
1 semaine |
1425 |
|
| A. Lechleiter |
PostDoc |
INRIA |
VIENNA |
conf. |
1 semaine |
1075 |
|
| Q. Chen |
PhD |
UDEL |
INRIA |
stage+conf |
1 mois |
2253 |
|
| G. Giorgi |
PhD |
Genova |
INRIA |
stage |
2,5 mois |
2999 |
|
| A. Cossonniere |
PhD |
TOULOUSE |
INRIA |
visite |
1 semaine |
244 |
|
| G. Giorgi |
PhD |
Genova |
UDEL |
ecole |
2 semaines |
|
1663 |
| A. Cossonniere |
PhD |
TOULOUSE |
UDEL |
ecole |
2 semaines |
|
1972 |
| A. Cossonniere |
PhD |
TOULOUSE |
UDEL |
stage |
3 mois |
|
4000 |
(1) post-doc / doctorant / stagiaire
(2) colloque, thèse, stage,
visite....
(3) précisez l'unité (mois, semaine..)
III. PREVISIONS 2010
Programme
de travail
Description du programme scientifique de
travail pour l'année 2010
The program for 2010
will be a
continuation of the studies started in 2008 and further developed in
2009, focusing on the use of
transmission
eigenvalues in inverse scattering theory and the imaging of anisotropic
coatings as well as the investigation of the remaining questions
proposed in our
program, such as
asymptotic models for unbounded media and their use in the imaging of
buried objects. We shall also pursue our investigations on the
extension of current techniques
to more
challenging time dependent problems.
More specifically we will adress the following points:
- Transmission
eigenvalues and their use in inverse scattering problems: The result in the works mentioned above
have answered the important question of existence and discretness of
transmission eigenvalues for the scalar problem. An ongoing project, in the framework of A.
Cossonniere PhD thesis aims at extending these results to the full
electromagnetci problem. It would also be of great
interest to improve the lower bounds on the
index of refraction of the scattering object in terms of these
eigenvalues (numerical results have shown that available estimates are
far from being optimal). We recall that this type of result is
very
important for target identification problems where no a priori
knowledge is available on the physical nature of the scatterers.
This is the case for instance in most of
the urban infrastructure imaging problems since the objects lying
beneath the surface of an urban environment range
from abandoned facilities, rock formations and unmarked burial sites to
corroded chemical waste
deposits. In particular, a priori assumptions on the material or
topological properties of such objects
would be totally unrealistic.
First investigations are ongoing with G. Giovanni (PhD thesis): could
one numerically obtain improved estimates by solving a generalized
eigenvalue problem, where the eigenvalue represents the contrast (and
not the frequency of the wave). In the case of constant coefficient and
for the exact geometry this procedure would provide the exact value of
the index. The theoretical justification of this algorithm requires a
monotonicity argument of the transmission eigenvalues with respect to
the contrast, which is also under investigation.
Related problems with practical
interests that we plan to investigate, are the analysis of the interior
transmission problem and the corresponding eigenvalues in the case when
the contrast of the scattering object changes sign as well the investigation of complex
transmission eigenvalues which will enable us to extend the above ideas
to absorbing scatterers.
We also plan to pursue our goal to improve the numerical algorithm that
has
been designed to compute
transmission eigenvalues. More investigations are needed to explain the
observed instability in the cases of limited aperture data. A first
step has been done in this direction by providing a rigorous proof of
the norm of
the solution must blow up at resonant frequencies. Furthermore, the
results for
the scalar case need to be extended to the full
electromagnetic case.
- Finalization of our
investigations on the extension of the Linear Sampling Algorithm to
time dependent data to treat the case of scattering from perfect
conductors and the extention of
this approach to penetrable media. Furthermore,
we plan to examine the benefit of using time domain data with
respect to monchromatic data, for instance by the possibility of
reducing the number of measurement points.
- The investigation of
the problem
of the imaging of a perfectly conducting object coated by a thin
anisotropic dielectric layer as well as the analogous problem for a
dielectric object coated by a thin highly conducting anisotropic layer.
Such
problems arise for instance in corrosion detection and identification
problems where one needs to
distinguish between real targets and coated decoys. First studies
have been conducted sperately in each group. For instance
Bourgeois-Haddar have studied the uniqueness and stability of
reconstructing a generalized impedance boundary condition from a single
measurement (submitted article). Parellel
to this work, Cakoni-Monk have studied the inverse problem for an
obstacle with anisotropic impedance boundary condition (paper near
completion). In particular, they have proven uniqueness results and
have derive an integral equation for determining the matrix surface
impedance. N. Chaulet started a PhD thesis in the Defi group on
the reconstruction of generalized anisotropic boundary condition and
would profit from this associated team to combine the approches
developed in each side to solve his problem.
Long time perpectives
- Extend the gap reciprocity method for detecting buried objects in
a piecewise homogeneous background to the case of a fully
nonhomogeneous background (which is the case in most practical
applications). We will begin by investigating
theoretical questions linked with the justification of the method in
this case, in particular the construction of a dense set of
test functions. On the numerical side, the main problem will be
to
efficiently compute the Green tensor.
Some
special asymptotic cases, such as highly oscillating media (which may
constitute a very good approximation for relatively large wavelengths),
offer
the possibility to use an effective Green tensor (or homogenized
tensor). The incorporation of these ideas into the numerical
method offers a valuable
alternative to the full numerical computation of the Green tensor.
These considerations will be
addressed over a period of several years.
- Investigate the possibility of establishing
qualitative methods for studying imaging problems in the time domain
(at the present time all qualitative methods are essentially restricted
to the
frequency domain). This is an ambitious and
open ended project and only a common framework like
the Equipe associe would enable a significant progress in this
direction.
Programme d'échanges
avec budget prévisionnel
1. Echanges
- F. Cakoni, H. Haddar and A. Lechleiter plan to organize a two
days workshop on "inverse and optimization problems related to wave
propagation phenomena" during Spring 2010. This event will be sponsored
by the EADS-X-INRIA Chair MMSN (http://www.cmap.polytechnique.fr/mmnschair/index.html.
We plan to use part of the associated team money to invite our team
partners at UDEL to particpate to this event.
- A Cossonniere (PhD) will benefit from one month invitation to
visit UDEL and continue the studies started in 2009.
- N. Chaulet (PhD) will obtain money from the associated team for
a one month visit to UDEL.
- G. Giovanni (PhD) will get money from the associated team for a
one month visit to INRIA.
- One week visit (each) to UDEL for A. Lechleiter and H. Haddar .
| 1.
ESTIMATION DES DÉPENSES EN MISSIONS INRIA VERS LE PARTENAIRE |
Nombre de personnes
|
Coût estimé
|
| Chercheurs confirmés |
2 |
3000 |
Post-doctorants
|
|
|
| Doctorants |
2 |
6000 |
|
Stagiaires
|
|
|
Autre (précisez) :
|
|
|
|
Total
|
|
9000 |
| 2.
ESTIMATION DES DÉPENSES EN INVITATIONS DES PARTENAIRES |
Nombre de personnes
|
Coût estimé
|
| Chercheurs confirmés |
3 |
4500 |
Post-doctorants
|
|
|
| Doctorants |
1 |
3000 |
|
Stagiaires
|
|
|
Autre (conf) :
|
|
10000 |
|
Total
|
|
17500 |
2. Cofinancement
- The members of the Delaware team have
a grant from the U.S. Air Force Office of Scientific Research. Part of
this funding will be used to pay a one month training at UDEL for a Phd
student (2000 euros).
- The Department of Mathematical Sciences will provide supplementary
money for each
senior person of the team (Cakoni, Colton, Monk) toward travel expences
to visit INRIA (3000 euros).
- The MMSN Chair will provide money to support participation to the
workshop organized by F. Cakoni, H. Haddar and A. Lechleiter (10000
euros).
|
Commentaires
|
Montant
|
| A. Coût global de la
proposition (total des tableaux 1 et 2 : invitations, missions, ...) |
26500 |
| B. Cofinancements utilisés (financements
autres que Equipe Associée) |
15000 |
Financement "Équipe Associée"
demandé (A.-B.)
(maximum 20 K€ pour une 2e année et 10 K€ pour une 3e
année)
|
11500 |
Remarques ou observations :
© INRIA - mise à jour le
08/07/2009