Mean and variance of single photon counting with deadtime

The statistics of photon counting by systems affected by deadtime are poten tially important for statistical image reconstruction methods. We present a new way of analysing the moments of the counting process for a counter sys tem affected by various models of deadtime related to PET and SPECT imaging . We derive simple and exact expressions for the first and second moments o f the number of recorded events under various models. From our mean express ion for a SPECT deadtime model, we derive a simple estimator for the actual intensity of the underlying Poisson process; simulations show that our est imator is unbiased even for extremely high count rates. From this analysis, we study the suitability of the Poisson statistical model assumed in most statistical image reconstruction algorithms. For systems containing 'module s' with several detector elements, where each element can cause deadtime lo sses for the entire module, such as block PET detectors or Anger cameras, t he Poisson statistical model appears to be adequate even in the presence of deadtime losses.