Image reconstruction for bioluminescence tomography

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed by our group. While the forward imaging model is described by the diffusion approximation, BLT is the inverse problem to recover an internal bioluminescent source distribution subject to Cauchy data for the diffusion equation. This inverse source problem is ill-posed and does not yield the unique solution in the general case. The uniqueness problem under practical constraints was recently studied by our group. It was found that all the inverse source solutions can be expressed as the unique minimal energy source solution plus a non-radiating source. We demonstrate that the minimal energy source solution is not physically favorable for bioluininescence tomography, although the minimal energy constraint is utilized in other applications. To find a physically meaningful unique solution, adequate prior knowledge must be utilized. Here we propose two iterative approaches in this work. The first one is a variant of the well-known EM algorithm. The second one is based on the Landweber scheme. Either of the methods is suitable for incorporating knowledge-based constraints. We discuss several issues related to the implementation of these methods, including the initial guess and stopping criteria. Also, we report our numerical simulation results to demonstrate the feasibility of bioluminescence tomography.