Estimation of optical absorption in anisotropic background

Abstract

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