Section: Research Program

Inverse problems

Building on the strong expertise of POEMS in the mathematical modeling of waves, most of our contributions aim at improving inverse scattering methodologies.

We acquired some expertise on the so called Linear Sampling Method, from both the theoretical and the practical points of view. Besides, we are working on topological derivative methods, which exploit small-defect asymptotics of misfit functionals and can thus be viewed as an alternative sampling approach, which take benefit of our expertise on asymptotic methods.

An originality of our activity is to consider inverse scattering in waveguides (the inverse scattering community generally considers only free-space configurations). This is motivated at the same time by specific issues concerning the ill-posedness of the identification process and by applications to non-destructive techniques, for waveguide configurations (cables, pipes, plates etc...). In particular, with the help of experimental data obtained at CEA-List, we proved the feasibility of the Linear Sampling Method to identify defects in the context of ultrasonic NDT.

Lastly, we continued our work on the so-called exterior approach for solving inverse obstacle problems, which associates quasi-reversibility and level set methods. We extended such approach to evolution problems, in particular the wave equation in the time domain for a finite time interval.