Influence of malfunctioning block detectors on the calculation of single detector efficiencies in PET

In this work, we studied the artifacts generated by the application of methods of crystal efficiency calculation based on the fan-sum, to situations of high variability of efficiency, namely the cases of a ring with defective blocks and acquisitions using narrow energy windows. We propose two efficiency calculation methods to reduce these artifacts: one method discriminates the crystals with an efficiency very different from the average, and then uses a modification of the fan-sum to estimate the efficiency; the other method calculates iteratively the fan-sum of each crystal, weighted by the efficiencies of the opposed detectors. The effect of using an off-center uniform cylinder is also discussed, since it influences the performance of the algorithms. The proposed algorithms are compared with the more conventional fan-sum method and with an algorithm used in a commercial tomograph, using measurements and simulations. The results show a significant reduction of the efficiency estimation errors, in severe situations where detectors in a ring have very different detection efficiency.