Optical tomography in medical imaging

We present a review of methods for the forward and inverse problems in opti cal tomography. We limit ourselves to the highly scattering case found in a pplications in medical imaging, and to the problem of absorption and scatte ring reconstruction. We discuss the derivation of the diffusion approximati on and other simplifications of the full transport problem. We develop sens itivity relations in both the continuous and discrete case with special con centration on the use of the finite element method. A classification of alg orithms is presented, and some suggestions for open problems to be addresse d in future research are made.