The authors 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. They 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.
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Ferreira et al. (1999) studied this question.