Impact of Scatter Modeling Error on 3D Maximum Likelihood Reconstruction in PET

In statistical image reconstruction for PET, the reconstructed image quality depends on the system matrix as well as the scatter correction method used, especially for the case of a large attenuating medium where the measurement process is dominated by photon attenuation and scatter. Accurate system and scatter modeling can improve image quality, but whatever the method employed systematic and/or random errors will always exist in the system model, inevitably impacting final reconstructed image quality. Theoretical expressions have been derived to study the error propagation from the scatter response function to the reconstructed images for the case of maximum likelihood (ML) reconstruction. The effect of system and scatter modeling errors for three different scatter correction methods are considered: a) scatter subtraction, b) adding scatter as a constant term to the forward model and c) a unified model where the scatter is completely modeled within the system matrix itself. First order approximations are used to derive the theoretical expressions for the error propagation, which account for errors in both the system matrix and the scatter estimates (when used outside the system matrix). These expressions are validated using simulated data. A close agreement is found between the measured and theoretically derived error images, with the unified system model being least sensitive to the errors. The theoretical expressions are useful to determine the required accuracy for the system matrix and scatter estimation.