Estimation of optical absorption in anisotropic background

In this paper we present a model for anisotropic light propagation and reconstructions of optical absorption coefficient in the presence of anisotropies. To model the anisotropies, we derive the diffusion equation in an anisotropic case, and present the diffusion matrix as an eigenvalue decomposition. The inverse problem considered in this paper is to estimate the optical absorption when the directions of anisotropy are known, but the strength may vary. To solve this inverse problem, two approaches are taken. First, we assume that the strength of anisotropy is known, and compare maximum a posteriori reconstructions using a fixed value for the strength when the value for the strength is both correct and incorrect. We then extend the solution to allow an uncertainty of the strength of the anisotropy by choosing a prior distribution for the strength and calculating the marginal posterior density. Numerical examples of maximum a posteriori estimates are again presented. The results in this paper suggest that the anisotropy of the body is a property that cannot be ignored in the estimation of the absorption coefficient.