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Expansion Methods Habib Ammari

Summary: Expansion Methods
Habib Ammari
Hyeonbae Kang
The aim of this chapter is to review recent developments in the math-
ematical and numerical modelling of anomaly detection and multi-physics
biomedical imaging. Expansion methods are designed for anomaly detec-
tion. They provide robust and accurate reconstruction of the location and
of some geometric features of the anomalies, even with moderately noisy
data. Asymptotic analysis of the measured data in terms of the size of the
unknown anomalies plays a key role in characterizing all the information
about the anomaly that can be stably reconstructed from the measured
data. In multi-physics imaging approaches, different physical types of
waves are combined into one tomographic process to alleviate deficiencies
of each separate type of waves, while combining their strengths. Muti-
physics systems are capable of high-resolution and high-contrast imaging.
Asymptotic analysis plays a key role in multi-physics modalities as well.
1 Introduction 3
2 Electrical Impedance Tomography for Anomaly Detection 4


Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics