Determining the absorption in anisotropic media

Gaburro, Romina and Lionheart, William (2010) Determining the absorption in anisotropic media. [MIMS Preprint]

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Abstract

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 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User:	Prof WRB Lionheart
Date Deposited:	12 Oct 2010
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1530

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