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Expansion Methods

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Handbook of Mathematical Methods in Imaging

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Abstract

The aim of this chapter is to review recent developments in the mathematical and numerical modeling of anomaly detection and multi-physics biomedical imaging. Expansion methods are designed for anomaly detection. 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. Multi-physics systems are capable of high-resolution and high-contrast imaging. Asymptotic analysis plays a key role in multi-physics modalities as well.

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Authors and Affiliations

  1. Department of Mathematics and Applications, Ecole Normale Supérieure, Paris, France

    Habib Ammari

  2. Department of Mathematics, Inha University, Incheon, Korea

    Hyeonbae Kang

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  1. Habib Ammari
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  2. Hyeonbae Kang
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Correspondence to Habib Ammari or Hyeonbae Kang .

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  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Ammari, H., Kang, H. (2015). Expansion Methods. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_47

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