A modeled point spread function for a noise-free system matrix

Iterative image reconstruction, can provide significant improvements in both image signal-to-noise ratio and spatial resolution when compared to linear methods such as filtered back-projection. Besides modeling Poisson noise, one of the key advantages of iterative image reconstruction is the ease of incorporation of detailed models of the system response. These models are typically obtained with Monte Carlo simulations, which can be computationally very expensive and introduce noise in the data, while being inflexible. In this work, we develop a fully parameterized analytical model, which in combination with relatively short Monte Carlo simulations, yields the spatially variant point spread function for a prototype pre-clinical PET scanner. The model is adaptable for small variations of pixel pitch, without the need for new Monte Carlo simulations, and can also easily incorporate results from physical measurements, which often differ from simulations in a systematic way. We demonstrate results from using this model in reconstructions of Monte Carlo simulated phantom data, as well as in-vivo data acquired with the prototype pre-clinical PET scanner.