Data-driven Estimation of Crystal Efficiencies using Single Events

Normalization correction is a pre-requisite for accurate reconstruction of PET images. Uniform phantoms are often used to estimate normalization factors. While this approach can provide reliable results, the additional phantom-based scans reduce overall patient throughput. The main component in the normalization factors that may change over time is the crystal efficiencies. The crystal efficiencies affect both coincidence events and single events. Single events are used to provide additional data for estimating crystal efficiencies. A maximum-likelihood-based approach has been derived and used for the estimation of crystal efficiencies, which indicates that the crystal efficiency can be derived by dividing the measured single events with the estimated single events from activity distribution and attenuation map. An alternate update approach has been developed, where the activity distributions and the crystal efficiencies are jointly estimated. 2D simulations with different noise levels were employed to validate the method. Phantom scan using the partially developed EXPLORER system (two detector units) were also carried out. Fast Monte Carlo simulations were applied for acquiring the estimated single events from activity distributions. Noise-free simulations suggested that the proposed method can quantitatively recover the unknown crystal efficiencies. Noisy simulations suggested that high accuracy can still be achieved (~1% error) with noisy data. The study using the physical scan indicated that it is practical to acquire the measured and estimated singles, and the crystal efficiency map can be acquired using our method. We have proposed a method that can estimate crystal efficiencies using single events and routine clinical data. More studies using acquired data from the scanner will be conducted to further validate the method. This method makes it possible to reduce the number of phantom-based scans for quality control purposes.