The aim of this research is to improve the existing imaging algorithm for Optical Tomography. In this thesis we have taken two approaches to the problem. In the first approach we introduce a \emph{full maximum likelihood} (FML) method which estimates the noise level concurrently. We show that FML in combination with a proposed method of \emph{hold-out validation} is able to determine a nearly optimal estimate without overfitting to the noise in the data.
In the second approach, we will propose a Bayesian method that uses the so-called normal-Wishart density as a parametric prior. We will show that for low degrees of freedom this choice of prior has robust imaging properties and that in some cases the prior can even increase the image resolution (compared to the ML image) but still retain good suppression of noise. We show how \emph{graphical modelling} can assist in building complex probabilistic models and give examples for the implementation using a developed C++ library.
Throughout the thesis, methods are validated by reconstruction examples using simulated data. In the final chapter, we will also present images from real experimental data.