Compensation for geometric mismodelling by anisotropies in optical tomography

We propose an approach for the estimation of the optical absorption coefficient in medical optical tomography in the presence of geometric mismodelling. We focus on cases in which the boundaries of the measurement domain or the optode positions are not accurately known. In general, geometric distortion of the domain produces anisotropic changes for the material parameters in the model. Hence, geometric mismodelling in an isotropic case may correspond to an anisotropic model. We seek to approximate the errors due to geometric mismodelling as extraneous additive noise and to pose a simple anisotropic model for the diffusion coefficient. We show that while geometric mismodelling may deteriorate the estimates of the absorption coefficient significantly, using the proposed model enables the recovery of the main features.