Simultaneous reconstruction of internal tissue region boundaries and coefficients in optical diffusion tomography

In this paper we propose a new numerical method to the inverse problem in optical diffusion tomography. We consider the reconstruction of the diffusion and absorption coefficients (kappa, mu(a)) within a domain omega which is known to consist of a set of disjoint regions of distinct tissue types. The assumption is that the regions of different tissues are bounded by smooth boundary curves and have constant absorption and diffusion coefficients. The goal in the proposed method is to reconstruct simultaneously the boundaries of the tissue regions together with the absorption and diffusion coefficients within these regions. The solution of the problem is based on the finite element method and subdivision of the elements. The performance of the proposed method is evaluated by simulations in which the optical parameters (kappa, mu(a)) are relevant in medical applications of optical tomography. It is shown that the proposed method is able to recover both the boundaries and the coefficients with good accuracy.