Reverse differentiation and the inverse diffusion problem

In this paper the task of solving the inverse photon diffusion problem in human tissue will be discussed. In such problems the optical properties of the tissue are to be determined from a knowledge of measured values of boundary output fluxes. A finite element model is proposed for the solution process and the problem is posed as a least squares optimisation problem. An important and costly part of optimisation processes is the calculation of gradients of the merit function. It has been shown that for such problems the reverse differentiation process can be implemented very efficiently with significant savings in both computation time and store. In this paper we show that the finite element optimisation process with reverse differentiation is ideally suited to the solution of the inverse diffusion problem.