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Imaging in Random Media

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Handbook of Mathematical Methods in Imaging

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Abstract

We give a self-contained presentation of coherent array imaging in random media, which are mathematical models of media with uncertain small-scale features (inhomogeneities). We describe the challenges of imaging in random media and discuss the coherent interferometric (CINT) imaging approach. It is designed to image with partially coherent waves, so it works at distances that do not exceed a transport mean-free path. The waves are incoherent when they travel longer distances, due to strong cumulative scattering by the inhomogeneities, and coherent imaging becomes impossible. In this article we base the presentation of coherent imaging on a simple geometrical optics model of wave propagation with randomly perturbed travel time. The model captures the canonical form of the second statistical moments of the wave field, which describe the loss of coherence and decorrelation of the waves due to scattering in random media. We use it to give an explicit resolution analysis of CINT which includes the assessment of statistical stability of the images.

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Acknowledgements

This article reviews results obtained in collaboration with Josselin Garnier from Université Paris VII, George Papanicolaou from Stanford University, and Chrysoula Tsogka from University of Crete. These results are published in [8, 9, 11, 12]. The work of L. Borcea was partially supported by the AFSOR Grant FA9550-12-1-0117 and the ONR Grant N00014-14-1-0077.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 530 Church Street, 48109, Ann Arbor, MI, USA

    Liliana Borcea

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  1. Liliana Borcea
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Correspondence to Liliana Borcea .

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

    Otmar Scherzer

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Borcea, L. (2014). Imaging in Random Media. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27795-5_41-2

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  • DOI: https://doi.org/10.1007/978-3-642-27795-5_41-2

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  • Online ISBN: 978-3-642-27795-5

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