Direction des
Relations et Internationales (DRI)
Programme
INRIA "Equipes Associées"
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 Futurs Saclay
Thème INRIA : NumD |
Pays : France |
| |
Coordinateur
français
|
Coordinateur
étranger
|
| Nom, prénom |
HADDAR Houssem |
CAKONI Fioralba |
| Grade/statut |
CR1 (Habilitation) |
Associated Professor |
Organisme d'appartenance
|
Equipe DeFI (Equipe commune INRIA Futurs/Ecole Polytechnique) |
Mathematical Department of the 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 |
|
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 oppose 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 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 gap 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.
|
Présentation
de l'Équipe Associée
1. Présentation du coordinateur étranger
Dr. Fioralba Cakoni received her Ph.D in mathematics in 1996
form the University of Tirana and University of Patras.
During 1998-2000 she was an Alexander von Humboldt postdoctoral fellow
at the University of Stuttgart, Germany. Since 2000 she has been
in the Department of Mathematical Sciences
at the University of Delaware, where she now holds a tenured Associate
Professor position. She has writen 30 papers in refereed journals and
several conference proceedings. She is the co-author with David Colton
of the book titled "Qualitative Methods in Inverse Scattering Theory"
published by Springer in 2006. She has given numerous invited
talks at international conferences and at many universities. For a
detailed account on her research please visit F. Cakoni web site.
2. Historique de la collaboration
-
2.1. entre les
équipes : The collaboration
between the inverse
scattering group at the University of Delaware (formed by P. Monk, D. Colton
and F. Cakoni) and H. Haddar at INRIA
was initiated by the appointment of Dr. Haddar to a Post-Doc
posision at the University of Delaware in 2001 followed by continous
collaboration since then. This collaboration has been intense and
fruiteful: It has led to the
development of the linear sampling method in inverse electromagnetic
scattering theory, the introduction of the gap reciprocity method for
the detection of buried objects and an investigation of the basic
theory of transmission eigenvalues and their application to
electromagnetic inverse scattering theory. These advances have been
facilitated by numerous visits in recent years between researchers at
INRIA and Delaware which were funded by the host institutions. Common
publications contains a list of 8 articles in top
mathematical journals, 3 technical reports and 4 international
conference proceedings. The full list can be found in the web
page of the
participants to this associated team. The following is a partial list
of some of our significant papers:
- F. Cakoni, D. Colton and H.
Haddar, The computation of lower bounds for the norm of the index of
refraction in an anisotropic media, J.
Integral Equations and Applications, (to appear).
- F. Cakoni and H. Haddar, A
variational approach for the solution of electromagnetic interior
transmission problem for anisotropic media, Inverse Problems and Imaging, 1, No 3, 443-456 (2007).
- F. Cakoni, MB. Fares and H. Haddar, The
electromagnetic
inverse scattering problem for buried objects in a known
inhomogeneous background, Inverse
Problems, 22, 845-867
(2006).
- D. Colton and H. Haddar, An
application of the
reciprocity gap functional to inverse scattering
theory, Inverse Problems, 21, 383-398 (2005).
- H.
Haddar and P. Monk, The linear sampling method for
solving the electromagnetic inverse medium problem, Inverse Problems, 18, pp. 891-906, (2002).
3. Impact :
- 3.1. Impact on existing collaboration with
the
Department of Mathematical Sciences of the University of Delaware:
The
research team at Delaware together with Dr. Haddar at INRIA are among
the leading researchers in the world in the emerging field of
qualitative methods in electromagnetic inverse scattering theory and
their unique combination of analytical and numerical skills has gained
them international recognition. The further development of this new
approach to imaging together with the application of these new
techniques to the problems proposed in the Scientific Program can only
be accomplished by an active and ongoing collaboration between the
research groups at INRIA and the University of Delaware. The scientific importance of an
associated team is due to the following reasons:
First, it is important to emphasize that the field of inverse
scattering has entered a phase of maturity in which associated
teams offer an ideal framework to further our national and
international visibility and to greatly facilitate our interaction with
the industrial world on both sides of the Antlantic.
Second,
the research program that we are proposing is more involved than
in our previous collaboration
and will certainly require hiring new PhD students and Post-Docs. The
financial support from the "equipe
associee" will provide a big help
in this direction by giving us the opportunity to hire Master Degree
students and
then offer them the opprtunity afterwards to persue co-directed
theses based on long term visits and scientific collaboration.
This is a crucial factor in maintaining viable interactions and
initiating
long-term research programs.
Finally, we note that this associated team will also facilitate
interaction with the optimization
component of the DEFI group, which we believe will encourage the
development of clever hybrid methods that combine the efficiency of
sampling
techniques with the accuracy of minimization algorithms.
- 3.2. Impact on collaborations with other
INRIA
teams: H. Haddar and P. Monk have active
collaborations with the INRIA project-team POEMS on forward solvers for
scattering problems. The creation of this associted team will certainly
strengthen this ongoing collaboration.
II. PREVISIONS 2008
Programme
de travail
Detailed scientific program for 2008: Particular attention will
be placed on the use of transmission
eigenvalues in inverse scattering theory, the imaging of anisotropic
coatings
and the use of the gap reciprocity principle in the detection of buried
objects. We shall also investigate the extension of current techniques
to more
challenging time dependent problems.
More specifically we will adress the following points:
- Study the existence of transmission
eigenvalues for Maxwell's
equations and investigate their use in establishing lower bounds on the
index of refraction of the scattering object. 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.
The numerical algorithm that has been designed to compute
transmission eigenvalues needs more investigation since we have
observed instability in the cases of limited aperture data. Present
results for the scalar case need to be extended to the full
electromagnetic case. We plan to propose a training program for
Master Degree students related to the numerical aspects of this problem.
- Consider 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 from coated decoys. We shall study
both the forward and
inverse
problems.
For the forward problem, the first step consists in extending the
asymptotic models developed within the
DeFI team to the anisotropic case (which fits more to realistic cases).
The
second step will be the
incorporation of these models into a forward solver which is either
based on integral
equation methods (which will be conducted in collaboration with
Cerfacs) or on
a volumic discretization approach such as the ultra weak
formulation developed by P. Monk.
For the inverse problem, the methods previously developed at Delaware
and INRIA on the identification
of a constant surface impedance needs to be extended both to the case
of an anisotropic surface impedance as well as the case of
generalized impedance
boundary conditions where the impedance operator is a second order
differential boundary operator. The latter case will be studied in the
framework
of a training program for Master Degree students.
- 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.
Budget prévisionnel
2008
1. Co-financement
- The participants from the Delaware team have
grant from the U.S. Air Force Office of Scientific Research. Part of
this funding will be used to pay for one trip per year for a person at
INRIA to Delaware.
- The Department of Mathematical Sciences will provide money for each
senior person of the team (Cakoni. Colton, Monk) per year from
Dealaware to travel to INRIA.
| ESTIMATION
PROSPECTIVE DES CO-FINANCEMENTS |
|
Organisme
|
Montant
|
| AFSOR |
1000 Dollars per year
|
| UDEL |
3000 Dollars per year
|
| |
|
| |
|
| |
|
|
Total
|
4000 Dollars per year |
2. Echanges
- Visits, Missions: It is hard
to provide at this time a precise calendar. However, we anticipate
regular visits of
members of the associated team (Cakoni, Colton and Monk) and their
students to INRIA together with visits of Dr. Haddar and the DeFI team
members
to Delaware.
- We expect to hire at least two Master Degree students for
training at INRIA on subjects related to the program of 2008 with the
possibility of
continuing into PhD studies that will be co-directed by H. Haddar and
F. Cakoni.
- We plan to jointly organize an international conference on
inverse scattering
problems in May 2008 Honoring the work accomplished by D. Colton and
R. Kress with whom we also have intense collaboration (see the web page of
the conference). This conference will certainly be an excellent
occasion to advertise for our associated team in the inverse scattering
community. Some
funding will be used for travel and the accomodation expenses of a few
invited
speakers.
| ESTIMATION
DES DÉPENSES |
Montant
|
| |
Nombre
|
Accueil
|
Missions
|
Total
|
| Chercheurs confirmés |
4 |
4000 |
2000 |
6000 |
Post-doctorants
|
1 |
1000 |
1000 |
2000 |
| Doctorants |
1 |
1000 |
1000 |
200 |
|
Stagiaires
|
2 |
9000 |
|
9000 |
Autre: ICISP conf
|
|
|
|
4000 |
|
Total
|
|
|
|
23000 |
| |
|
- total des
co-financements
|
3000 |
| |
Financement "Équipe
Associée" demandé
|
20000 |
© INRIA - mise à jour
le 28/08/2007