Description

The workshop "Inverse problems and imaging" took place in Paris
at the Institut Henri Poincaré on February 20-22, 2013. It was
organized under the auspices of the French Mathematical Society
(SMF) as a session of the "États de la recherche". Its main
objective was to present recent developments on inverse problems
and imaging. Most of these developments result from interactions
between several domains of mathematics: analysis and control of
partial differential equations, stochastic analysis, statistics, multiscale
analysis. The three mini-courses given by Liliana Borcea
(University of Michigan, USA), Hyeonbae Kang (Inha University,
Korea), and Gunther Uhlmann (University of Washington, USA) can
be considered as perfect illustrations of these fruitful interactions.
Liliana Borcea addresses sensor array imaging in random media,
more exactly in randomly perturbed waveguides. She introduces
different imaging methods and study their resolution and stability
properties. In his lecture Hyeonbae Kang reviews recent progress on
imaging by generalized polarization tensors (GPTs), enhancement of
near-cloaking by GPT-vanishing structures, cloaking by anomalous
localized resonance, and analysis of stress concentration. He shows
how the Neumann-Poincaré operator naturally arises in all these
problems. Gunther Uhlmann considers transformation-optics based
cloaking in acoustic and electromagnetic scattering. He presents
various regularized approximate cloaking schemes.