Estimation of decoding error for light sharing based PET detector module using a Gaussian mixture model

Positron emission tomography (PET) is typically based on 2-D array of scintillation crystals and light sharing technique decoded by Anger-logic. The decoded result is a pseudo-position of the gamma interaction. A crystal position map generated from the flood histogram is used as a crystal look-up table (CLT) to assign each pseudo-position to a specific crystal. For the light sharing based PET detector module, the crystal responses overlap each other, which introduces position decoding error. In this paper, the position decoding error was quantitatively calculated by decoding error ratio (DER), which was defined as the probability of the events of one crystal assigned to others. The calculation method was based on the Gaussian mixture model (GMM) and CLT. Firstly, the flood histogram was estimated by GMM. A calculation from the segmentation results of a neighborhood standard deviation (NSD) based algorithm was applied to estimate the parameter initial values. Then, three CLTs generated by manual segmentation, by GMM and by a NSD based algorithm were applied to calculate DERs. The results showed that the CLT generated by the GMM and NSD based algorithm achieved lower DERs, which are expected to get higher spatial resolution. The detector spatial resolution is affected by DERs, however it is not quantitatively studied in the earlier literatures. In the future work, we will improve the spatial resolution estimation function including the decoding error factor with a function of DERs.