A popular method for gamma ray detection utilizes scintillation detectors which consist of crystals optically coupled to a photomultiplier tubes (PMTs). Scintillators are widely used in the medical radiation fields such as CT scanners, gamma cameras and positron emission tomography (PET) scanners -. The scintillation crystal responds to the absorption of gamma ray by the emission of a light pulse. This light pulse is characterized by the special properties of the crystal such as the decay time constant. Then the PMT generates an electrical pulse relative to the absorbed gamma energy.
The phenomenon known as a parallax-error or depth-of-interaction (DOI) error  which reduces the sensitivity and reconstruction quality of PET, most probably happened when the photons enter to the detector with non-perpendicular angle. Phosphor sandwich (phoswich) detectors  are considered as one of the methods used to reduce the parallax-error.
The phoswich detector is a stack of two or more different scintillation crystals; i.e. with different decay time constants, optically coupled to a single PMT. Hence the DOI error is reduced when the scintillated crystal is identified. The crystal identification (CI) requires applying one of the pulse shape discrimination (PSD) methods  - .
Different PSD algorithms were developed which can be classified into two categories: time domain and frequency domain. In the time domain, the cross correlation , fuzzy logic  and neural network  were employed in the PSD and CI methods. On the other hand, the Fast Fourier Transform (FFT) of the pulses improved the CI performance . Moreover, the normalized least sample (NLS) method , which is dependent strongly on one sample, reduced the FFT complexity at the expense of performance. Other researchers suggested a discrete wavelet (DWT) decomposition of the pulses as an alternative , , ,  to obtain a moderate complexity and a good performance. Also, two CI techniques based on the principle component analysis (PCA)  and the discrete cosine transform (DCT)  were developed.
Recently, the Zernike moments (ZMs) borrowed from pattern recognition field , , , were applied to identify the scintillating crystal type . In this approach, the ZMs vector represents the extracted features of the pulse and is classified by the Euclidean distance. The 2D-ZM CI method has the highest identification performance among other recent methods but it is too complex to fulfill the real time requirements of PET scanners .
The real time rate of PET events varies from system to another corresponding to the number of detectors and the hardware configurations. According to the ClearPETTM system , , one recorded event covers a 400 ns time window and the FPGA board which preprocesses and records events, needs 250 ns of dead time until it is ready to accept the next event. In other words, each event...