The successful development and clinical use of instruments that perform real-time near-infra red spectroscopy of transilluminated tissue has led to a widespread interest in the development of an imaging modality. The most promising approach uses picosecond laser pulses input on an object (Omega) , and measures the development of light intensity as a function of time at points on the boundary (partial)(Omega) . The imaging problem is to reconstruct the absorption and scattering coefficients inside (Omega) . We have proposed the following method for the reconstruction algorithm: A Forward model is developed in terms of the Green's Function of the Diffusion Approximation to the Radiative Transfer Equation. Given a perturbation of the image, the Jacobian of the Forward model can be derived. Inversion of the Jacobian then gives a perturbation step for a subsequent iteration. Previously we have derived an analytical expression for the Green's Function in certain simple geometries, and for a homogeneous initial image. We have now developed a Finite Element method to extend this to more general geometries and inhomogeneous images, with the inverse of the system stiffness matrix playing the role of the Green's Function. Thus it is now possible to proceed past the first iteration. The stability of the reconstruction is presented both for the time-independent case where the data is the absolute intensity on the boundary (partial)(Omega) , and for the time-dependent case where the data is the mean time of arrival of light.