As one of the emerging optical molecular imaging modalities, bioluminescence tomography is for reconstruction of the light source distribution inside a small animal body from the measured photon data on its surface. Such a light source distribution can be either induced through the excitation of an external light source, or generated by an internal bioluminescent source. The propagation of light within a biological medium is accurately described by the radiative transfer equation.
In this thesis, a bioluminescent source recovery problem is considered for the steady state radiative transfer equation. The recovery model is based on the minimization of combined effects of equation residual, boundary condition residual, and boundary measurement residual. The total variation of the light source is taken as one of the regularization terms so that the minimization of surface area of a light source is achieved. An alternating direction multiplier method is applied to decouple the system governing the light distribution and source data. Three different formulations and algorithms are introduced for the total variation regularization term. Convergence analysis is provided for each algorithm and numerical experiments are presented to show the performance of the algorithms.