A reconstruction algorithm for ultrasound-modulated diffuse optical tomography

Habib Ammari (1) , Emmanuel Bossy (2) , Josselin Garnier (3, 4) , Loc Hoang Nguyen (1) , Laurent Seppecher (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 ESPCI Paris - Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris
3 LJLL - Laboratoire Jacques-Louis Lions
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: imaging in complex media

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Habib Ammari, Emmanuel Bossy, Josselin Garnier, Loc Hoang Nguyen, Laurent Seppecher. A reconstruction algorithm for ultrasound-modulated diffuse optical tomography. Proceedings of the American Mathematical Society, 2014, 142 (9), pp.3221-3236. ⟨10.1090/S0002-9939-2014-12090-9⟩. ⟨hal-01017794⟩