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2010.89: Determining the absorption in anisotropic media

2010.89: Romina Gaburro and William Lionheart (2010) Determining the absorption in anisotropic media.

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Abstract. The problem in Optical Tomography of determining the spatially dependent absorption coefficient in an anisotropic medium with a-priori known strong scattering is considered. The problem is modelled by the diffusion approximation of the Radiative Transfer Equation and the time-harmonic case is studied. In this particular situation the diffusion approximation leads to an elliptic second order partial differential equation with complex variable coefficients which allows to treat the problem equivalently to the inverse conductivity problem in Electrical Impedance Tomography (EIT). Results of uniqueness and stability for the absorption coefficient are proven by using the approach of the work in SIAM J. Math. Anal. 33 (2001), no. 1, 153–171 for the inverse conductivity problem in EIT.

Item Type:MIMS Preprint
Uncontrolled Keywords:near infra-red scattering absorption tomography, anisotropic inverse problem
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 78 Optics, electromagnetic theory
MIMS number:2010.89
Deposited By:Prof WRB Lionheart
Deposited On:12 October 2010

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