Determining the absorption in anisotropic media

The problem in Optical Tomography of determining the spacially 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