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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A reconstruction algorithm for ultrasound-modulated diffuse optical tomography
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by Habib Ammari, Emmanuel Bossy, Josselin Garnier, Loc Hoang Nguyen and Laurent Seppecher PDF
Proc. Amer. Math. Soc. 142 (2014), 3221-3236 Request permission

Abstract:

The aim of this paper is to develop an efficient reconstruction algorithm for ultrasound-modulated diffuse optical tomography. In diffuse optical imaging, the resolution is in general low. By mechanically perturbing the medium, we show that it is possible to achieve a significant resolution enhancement. When a spherical acoustic wave is propagating inside the medium, the optical parameter of the medium is perturbed. Using cross-correlations of the boundary measurements of the intensity of the light propagating in the perturbed medium and in the unperturbed one, we provide an iterative algorithm for reconstructing the optical absorption coefficient. Using a spherical Radon transform inversion, we first establish an equation that the optical absorption satisfies. This equation together with the diffusion model constitutes a nonlinear system. Then, solving iteratively such a nonlinear coupled system, we obtain the true absorption parameter. We prove the convergence of the algorithm and present numerical results to illustrate its resolution and stability performances.
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Additional Information
  • Habib Ammari
  • Affiliation: Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France
  • MR Author ID: 353050
  • Email: habib.ammari@ens.fr
  • Emmanuel Bossy
  • Affiliation: Institut Langevin, ESPCI ParisTech, CNRS UMR 7587, 10 rue Vauquelin, 75231 Paris Cedex 05, France
  • Email: emmanuel.bossy@espci.fr
  • Josselin Garnier
  • Affiliation: Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13, France
  • Email: garnier@math.jussieu.fr
  • Loc Hoang Nguyen
  • Affiliation: Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France
  • Email: lnguyen@dma.ens.fr
  • Laurent Seppecher
  • Affiliation: Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France
  • Email: laurent.seppecher@ens.fr
  • Received by editor(s): February 8, 2012
  • Received by editor(s) in revised form: September 30, 2012
  • Published electronically: May 23, 2014
  • Additional Notes: This work was supported by the ERC Advanced Grant Project MULTIMOD–267184.
  • Communicated by: Walter Craig
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 3221-3236
  • MSC (2010): Primary 65R32, 44A12, 31B20
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12090-9
  • MathSciNet review: 3223378