MERCREDI 26 JANVIER 2011
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Mourad Sini
RICAM, Austrian Academy of Sciences
Altenbergerstrasse 69, A-4040, Linz, Austria

Title: Reconstruction of interfaces using multifrequency incident waves

Abstract: The talk is related to the inverse scattering by interfaces
for time-harmonic acoustic waves using few incident waves but with
many frequencies. We will report on the following three questions:
uniqueness, stability and reconstruction. A particular focus will be
on the link between these questions and some spectral properties of
the corresponding operator. We divide our talk into two main parts.

1. The first part is related to the case when we use only one
frequency. In this case, the answer to the first two questions
mentioned above is closely related to some isoperimetric inequalities
(as the Faber-Krahn inequality) for non smooth domains (non Lipschitz
domains).

2. The second part is related to the case when we use many
frequencies. In this case, one answer to the uniqueness question is
related to the limiting absorbtion principle and the absence of
eigenvalues for the corresponding operator. We also state some
stability estimates for low and high frequencies. Finally, we give a
multifrequency reconstruction algorithm which shows how taking into
account low as well as high frequency information on the far fields
provides good and stable reconstructions of the interfaces in contrast
to the case when we use far fields at a fixed frequency.