Image reconstruction for optical tomography using photon density waves

The forward model in this work is based on the frequency-dependent Diffusion approximation. The Diffusion approximation is solved using the Finite Element Method with the Robin Boundary condition. The model is two dimensional, with a circular domain simulating the cross section of a limb. The meshes are generated with FIDAP, a computational fluid dynamics package. The Diffusion matrix is solved using Cholesky decomposition, and results on the boundary for a modulated source include AC and DC data for a given set of optical parameters. The reconstruction is treated as a non-linear optimisation problem without constraints. The algorithm is developed using the least squares method. The errors between the measured and finite element values at the boundary are minimised by using the Conjugate Gradient and Truncated Newton methods. Forward Analytic Differentiation is used to calculate gradients. Images are reconstructed in the frequency domain for both a scattering and an absorbing object.