Calibration procedure for a DOI detector of high resolution PET through a Gaussian mixture model

A depth of interaction detector is developed for the next generation of positron emission tomography (PET) scanners. The detector unit consists of 8 × 8 crystal blocks with four layers of 2 × 2 Gd₂SiO₅:Ce arrays coupled to a 52 mm square position sensitive photomultiplier tube (PS-PMT). Each scintillation event is mapped in a two-dimensional (2-D) position histogram through the relative ratio of the output signals of the PS-PMT. To facilitate high spatial resolution imaging, accurate crystal identification is needed. A statistical model based on the approach of a Gaussian mixture model (GMM) is introduced for crystal identification. In the GMM, a cluster center and range attributed to individual peaks in the 2-D position histogram are defined. GMM can simultaneously estimate overlapping regions projected each crystal element. After block separation of 8 × 8 on the 2-D distribution, the crystal element regions are identified by the GMM in each block. The GMM method is applied two times, once for the cluster centers and once for determination of the range. These results are used to generate a look-up-table (LUT). This method successfully identified all crystal elements in the clustering area. By Monte Carlo simulation, we also proved that GMM method could choose LUT patterns to high resolution or high sensitivity with one parameter.