A modelling error approach for the estimation of optical absorption in the presence of anisotropies

Optical tomography is an emerging method for non-invasive imaging of human tissues using near-infrared light. Generally, the tissue is assumed isotropic, but this may not always be true. In this paper, we present a method for the estimation of optical absorption coefficient allowing the background to be anisotropic. To solve the forward problem, we model the light propagation in tissue using an anisotropic diffusion equation. The inverse problem consists of the estimation of the absorption coefficient based on boundary measurements. Generally, the background anisotropy cannot be assumed to be known. We treat the uncertainties in the background anisotropy parameter values as modelling error, and include this in our model and reconstruction. We present numerical examples based on simulated data. For reference, examples using an isotropic inversion scheme are also included. The estimates are qualitatively different for the two methods.