Monotonic iterative algorithms for crystal efficiencies estimation from normalization data and single rates estimation from compressed random coincidence data

PET scanner calibration is a routine procedure that is performed on a daily basis. The normalization data acquisition ideally should take as little time as possible. Consequently, normalization data are noisy and a component-based model is used to battle related issues. Most normalization components except scanner crystal efficiencies are fixed for a given scanner type. In this paper we propose a monotonic iterative algorithm for estimation of crystal efficiencies based on the Poisson Model. This model exploration leads to the necessary use of scatter distribution of a known subject in normalization data modeling. The proposed method produces a non-negative efficiencies solution. The update equation is a simultaneous type, which is easily parallelized. The method is applicable to compressed data, such as azimuthally (possibly TOF) mashed and axially (possibly TOF) rebinned data. The variance reduction of random coincidence data is a closely related problem due to a similar mathematical formulation. The proposed algorithm is directly applicable to this problem and is especially useful in compressed random data. Measured normalization and random data from a Siemens mCT scanner were used to validate the algorithm's performance. In normalization data, crystal efficiencies produced a less noisy estimate when compared to the currently-used mCT method. The use of scatter estimation improved uniformity of homogenous cylinder reconstruction. In random data, the proposed method estimation has an advantage in situations where data are missing (for example, due to block malfunctioning).