ARMAX-RLS Parameter-Estimation Crystal Identification in Phoswich PET Detectors

Some Positron Emission Tomography (PET) scanners achieve improved resolution or Depth-Of-Interaction (DOI) measurement using avalanche photodiode-based phoswich detectors, with different challenges (noise limitation) than traditional photomultiplier tubes (space limitation). DOI measurement is necessary in small-animal PET for parallax mitigation, while side-by-side phoswich detectors improve resolution without an equal increase in electronics complexity. Future improvements in scanner performance now require the improvement of the current Parameter Estimation (PE) digital Crystal Identification (CI) algorithms. Indeed PE CI becomes mandatory to the APD signal analysis of crystals with very similar scintillation properties (decay time difference less than ~15 ns), or when the Signal-to-Noise Ratio (SNR) is degraded, for Compton events with an energy below 150 keV, for instance. PE CI currently relies on one-parameter discrimination of crystal species after a Wiener parametric estimation of a pole-zero model. Neither that nor traditional Pulse-Shape Discrimination (PSD) can correctly accommodate the need for CI of low-energy scattered photons in very similar scintillation materials. This paper studies a Recursive Least-Squares (RLS) PE method based on Auto-Regressive Moving Average with exogenous variable (ARMAX) modeling of the acquisition chain conjugated with simultaneous 3-parameter CI adapted from Vector Quantization (VQ). The RLS algorithm presents a significant improvement for the discrimination of similar materials (~ 80% less primary CI error versus Wiener CI for 15 ns decay time difference) and excellent performance in heavy noise (negligible CI error for 0 dB SNR 30-keV BGO photons versus LSO). Issues remaining include the handling of noise through the exogenous variable and the computational burden, still too high for existing hardware.