Evaluation of maximum-likelihood position estimation with Poisson and Gaussian noise models in a small gamma camera

It has been reported that maximum-likelihood position estimation (MLPE) algorithms offer advantages of improved spatial resolution and linearity over conventional Anger algorithm in gamma cameras. While the fluctuation of photon measurements is more accurately described by Poisson than Gaussian distribution model, the likelihood function of a scintillation event assumed to be Gaussian could be more easily implemented and might provide more consistent outcomes than Poisson-based MLPE. The purpose of this study is to evaluate the performances of the noise models, Poisson and Gaussian, in MLPE for the localization of photons in a small gamma camera (SGC) using NaI(Tl) plate and PSPMT. The SGC consisted of a single NaI(Tl) crystal, 10 cm in diameter and 6 mm thick, optically coupled to a PSPMT (Hamamatsu R3292-07). The PSPMT was read out using a resistive charge divider, which multiplexes 28(X) by 28(Y) cross wire anodes into four channels. Poisson and Gaussian-based MLPE methods have been implemented using experimentally measured detector response functions (DRF). The averaged intrinsic spatial resolutions were 3.14, 3.09, and 2.88 mm, the integral uniformities were 15.3%, 12.3%, and 11.4%, and the averaged linearities were 0.75, 0.33, and 0.22 mm for Anger logic, Poisson, and Gaussian-based MLPE, respectively. MLPEs considerably improved linearity and uniformity compared to Anger logic. Gaussian-based MLPE, which is easy to implement, allowed to obtain better linearity and uniformity performances than the Poisson-based MLPE.