ARMAX model and recursive least-squares identification for DOI measurement in PET

Several attempts have been made at measuring DOI in PET scanners. Most solutions offer poor performance in noise. Others are overly complex in view of the information recovered. Most implementations are also impractical, if feasible at all, in APD-based, digital, small animal scanners using multilayer scintillation detectors. The computing power and low cost of modern digital electronics allows the use of more advanced techniques. This paper proposes a novel method derived from control theory that abstracts the scanner acquisition front-end measurement system into a single model. It fits an AutoRegressive Moving-Average with noise (ARMAX) model to the measured data using a Recursive Least-Squares (RLS) identification algorithm, with excellent performance in heavy noise. DOI is subsequently discriminated by the locus of identified poles and zeros onto a complex digital frequency map. More advanced decision heuristics can be used when the detector scintillation layers have too similar light output dynamics. The implementation of this algorithm in PET benefits from extensive a priori knowledge of the system, resulting in significant simplifications. The identification engine is realized on programmable logic chips (FPGA), is pipelined, is running at 100 MHz and is time-shared between several detectors. Preliminary simulations show near perfect discrimination of the scintillation layer. This paper discusses the theory, the implementation and the pros and cons of that method.