Realizing that the mathematical sciences can be critical to certain areas of
imaging, we organized a three-day workshop on mathematical and computational
challenges in imaging microstructures at the Institut Henri Poincar´ e in Paris from
the 18th to 20th of June, 2008.
The problems that appear in imaging microstructures pose signiﬁcant chal-
lenges to the mathematical community. They have attracted a lot of attention of
researchers lately. The methods involved come from a wide range of areas of pure
and applied mathematics ranging from potential theory to PDEs, to scattering
theory, to complex analysis, to numerical methods.
Due to the character of the topic of the workshop, not only prominent math-
ematicians actively working in imaging were invited, but also several outstanding
physicists who could communicate with mathematicians on the workshop issues.
The speakers were from diﬀerent ﬁelds: inverse problems, wave propagation, multi-
scale analysis, and the mathematical theory of composite materials. The goal of the
workshop was to merge their expertise to direct it towards challenging issues such
as robust algorithms for imaging defects in composite materials or the mathematics
of super-resolved imaging of microstructures.
The main purpose of this volume is to review the state-of-the-art developments
in imaging microstructures from analytic, numerical, and physics perspectives. We
envision that these proceedings will give insights regarding future research direc-
tions and stimulate much needed progress in this ﬁeld.
The tremendous success of the workshop was only possible thanks to the enthu-
siastic participation of wonderful speakers and authors of this volume. We thank
them all. We also thank the staﬀ at the Institut Henri Poincar´ e without whom
the workshop would not have been possible. Finally, we acknowledge the ﬁnancial
support of the ANR.
Habib Ammari and Hyeonbae Kang