Optimal non-linear line-of-flight estimation in positron emission tomography

Detection of high-energy photons emitted as the result of positron decay is one of the most important low-level stages in PET imaging. In this paper we consider a detector based on the Anger scintillation camera. Incident high-energy gamma quanta, generated due to positron decay, produce scintillation effect in the crystal. As a result, a shower of low energy photons in the visible and UV spectra is emitted. These photons are collected by an array of photo-multipliers (PMTs), optically coupled to the scintillation crystal, and invoke electric impulses in them. The PMT responses are utilized in estimation of the scintillation point coordinates. Our work incorporates side information on the photon incidence angle into the process of position estimation. We use localized, asymptotically optimal, nonlinear estimators, implemented by feedforward and radial basis function (RBF) neural networks. As a byproduct, we get accurate position estimation over the entire area of the detector including the edges. This is difficult to obtain with centroid arithmetic algorithms. We present a comparison of algorithms on a Monte Carlo simulation and discuss the prospects for practical implementation.