Improved numerical integration for analytical photon distribution calculation in SPECT

In this thesis we study an existing Analytic Photon Distribution (APD) method for SPECT imaging. The method uses multi-dimensional numerical integration to calculate photon propagation and detection probabilities for a SPECT camera system. This calculation is extremely time-consuming I the original implementation of the method. Fast computation of these probabilities is especially challenging for scattered photons, due to the large number of possible photon paths and method, however, can significantly improve the speed of the calculation. Replacing Romberg integration, which was used in the original implementation, with a Gaussian quadrature method allows us to greatly reduce the calculation time. The photon distributions generated using the improved quadrature method are in good agreement with those generated by the original program.