Preface
During the months of July and August 2010, a thematic program on mathe-
matical and statistical methods for imaging was held at Inha University, Korea. As
a part of the program, a three-day international conference was organized, at which
prominent experts in the field were invited. The lectures they delivered covered a
variety of hot topics of current research on imaging. Recent advances in imaging
are certainly consequences of innovative mathematical approaches to fundamental
issues such as detectability, resolution, and stability, as well as of a strong interest
in potential applications. These mathematical approaches include multi-scale an-
alytical and computational techniques, statistical methods, random matrix theory,
and signal theory.
A multi-scale approach plays a key role in imaging. It leads to effective and
robust reconstruction algorithms in many imaging problems since it allows us to
overcome the severe ill-posedness character of image reconstruction. The mathe-
matical tools involved come from a wide range of areas of pure and applied math-
ematics ranging from potential theory to PDEs, to scattering theory, to complex
analysis, to numerical methods. At the same time, a lot of effort has been devoted
to design new and efficient approaches for retrieving information from random me-
dia. These approaches promise to allow anomaly wave imaging in the presence of
both medium and measurement noises. Moreover, the recent use of random matrix
theory for defect imaging has added a new dimension to the field.
This volume provides a forum for a deeper and more unified understanding of
the field of imaging and for combining analytical and statistical tools in imaging.
It offers the reader a good overview of current research and direction for further
pursuit. Challenging problems are addressed from analytical, numerical, as well as
statistical perspectives. The objective of the volume is fourfold: (i) To analytically
investigate the robustness, with respect to incomplete data, measurement, and
medium noises of the recently developed multi-scale approaches; (ii) To establish
hypothesis testing and resolution analysis, particularly for anomaly detection;
(iii) To design new efficient imaging techniques; (iv) To take into account the effects
of anisotropy, dissipation, or attenuation in imaging.
The tremendous success of the workshop was only possible due to the enthu-
siastic participation of wonderful speakers and authors of this volume. We are
thankful to all of them. We also acknowledge with gratitude the generous support
from NIMS (National Institute for Mathematical Sciences) during the thematic
program. We would also like to thank the host institution—Inha University.
Habib Ammari, Josselin Garnier, Hyeonbae Kang, and Knut Sølna
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