Algorithms for calculating detector efficiency normalization coefficients for true coincidences in 3D PET

Accurate normalization of lines of response in 3D PET is a prerequisite for quantitative reconstruction. Most current methods are component based, calculating a series of geometric and intrinsic detector efficiency factors. We have reviewed the theory behind several existing algorithms for calculating detector efficiency factors in 2D and 3D PET, and have extended them to create a range of new algorithms. Three of the algorithms described are 'fully 3D' in that they make use of data from all detector rings for the calculation of the efficiencies of any one line of response. We have assessed the performance of the new and existing methods using simulated and real data, and have demonstrated that the fully 3D algorithms allow the rapid acquisition of crystal efficiency normalization data using low-activity sources. Such methods enable the use of scatter-free scanning line sources or the use of very short acquisitions of cylindrical sources for routine normalization.