Accurate geometric and physical response modelling for statistical image reconstruction in high resolution PET

Accurate modeling of the data formation and detection process in PET is essential for optimizing resolution. Here we develop a model in which the following factors are explicitly included: depth dependent geometric sensitivity, photon pair non-colinearity, attenuation, intrinsic detector sensitivity, non-uniform sinogram sampling, crystal penetration and inter-crystal scatter. Statistical reconstruction methods can include these modeling factors in the system matrix that represents the probability of detecting an emission from each image pixel at each detector-pair. We describe a method for computing these factors using a combination of calibration measurements, geometric modeling and Monte Carlo computation. By assuming that blurring effects and depth dependent sensitivities are separable, we are able to exploit rotational symmetries with respect to the sinogram. This results in substantial savings in both storage requirements and computational costs. Using phantom data we show that this system model can produce higher resolution near the center of the field of view, at a given SNR, than both simpler geometric models and reconstructions using filtered backprojection. We also show, using an off-centered phantom, that larger improvements in resolution occur towards the edge of the field of view due to the explicit modeling of crystal penetration effects.