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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A reconstruction algorithm for ultrasound-modulated diffuse optical tomography


Authors: Habib Ammari, Emmanuel Bossy, Josselin Garnier, Loc Hoang Nguyen and Laurent Seppecher
Journal: Proc. Amer. Math. Soc. 142 (2014), 3221-3236
MSC (2010): Primary 65R32, 44A12, 31B20
Published electronically: May 23, 2014
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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12090-9
PII: S 0002-9939(2014)12090-9
Keywords: Ultrasound-modulated optical imaging, diffuse optical tomography, spherical Radon transform, Helmholtz decomposition, reconstruction, convergence
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
Article copyright: © Copyright 2014 American Mathematical Society