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Photoacoustic Imaging for Attenuating Acoustic Media

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Mathematical Modeling in Biomedical Imaging II

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2035))

Summary

The aim of this chapter is to consider two challenging problems in photo-acoustic imaging. We consider extended optical sources in an attenuating acoustic background. We provide algorithms to correct the effects of imposed boundary conditions and that of attenuation as well. By testing our measurements against an appropriate family of functions, we show that we can access the Radon transform of the initial condition in the acoustic wave equation, and thus recover quantitatively the absorbing energy density. We also show how to compensate the effect of acoustic attenuation on image quality by using the stationary phase theorem.

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Acknowledgements

This work was supported by the ERC Advanced Grant Project MULTIMOD–267184.

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Authors and Affiliations

  1. Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France

    Habib Ammari & Vincent Jugnon

  2. Centre de Mathématiques Appliquées, CNRS UMR 7641, Ecole Polytechnique, 91128, Palaiseau, France

    Elie Bretin & Abdul Wahab

Authors
  1. Habib Ammari
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  2. Elie Bretin
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  3. Vincent Jugnon
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  4. Abdul Wahab
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Correspondence to Habib Ammari .

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Editors and Affiliations

  1. Mathématiques et Applications, École Normale Supérieure, rue d'Ulm 45, Paris, 75005, France

    Habib Ammari

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© 2012 Springer-Verlag Berlin Heidelberg

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Ammari, H., Bretin, E., Jugnon, V., Wahab, A. (2012). Photoacoustic Imaging for Attenuating Acoustic Media. In: Ammari, H. (eds) Mathematical Modeling in Biomedical Imaging II. Lecture Notes in Mathematics(), vol 2035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22990-9_3

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