Mean and Variance of Photon Counting with Deadtime

The statistics of photon counting by systems affected by deadtime are potentially important for statistical image reconstruction methods. We present a new way of analyzing the moments of the counting process for a counter system affected by various models of deadtime related to PET and SPECT imaging. We derive simple and exact expressions for the first and second moments of the number of recorded events under various models. From our mean expression for a SPECT deadtime model, we derive a simple estimator for the actual intensity of the underlying Poisson process; simulations show that our estimator is unbiased even for extremely high count rates