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A voxel-based approach to 3D PET analytic system modeling which projects the unit sphere of Klein-Nishina probabilities onto the cylindrical detection sphere, is proposed and under development. The aim is to offer the accuracy of a Monte Carlo model but without the noise and computational limitations. The model, incorporating both photon attenuation and scattering, defines PET system matrix elements based only on knowledge of a transmission scan and the specifications of a given PET system. No knowledge of the true activity is required to define the model. Reconstruction with such a unified analytic model makes full use of all the information contained in the measured data (both true and scatter events). No scatter subtraction, or scatter addition to the forward model output, are required. For 3D PET with large attenuating media, full use of the acquired information results in lower noise levels in the final image. The core of the technique models object scatter and attenuation via the Klein-Nishina cross-section and the transmission scan. However, the model must also include component-based normalization which accounts for scanner geometry as well as the crystal type and their arrangement.

Conventional methods for dealing with attenuation and scatter can degrade the reconstructed image quality, particularly if the attenuating medium is large (as in whole body 3D PET). In such cases, a substantial scatter subtraction is performed followed by amplification of the remaining data (to correct for attenuation), which results in noisy reconstructions. More recent methods used with iterative reconstruction include the attenuation in the system model in conjunction with either pre-scatter subtraction or a separate addition of the scatter component after each application of the forward model. This work compares these more conventional approaches to including attenuation and scatter within the EM algorithm with a fully unified scatter and attenuation model - whereby all attenuation and scattering effects are included within the system matrix. For this case all acquired data are used and regarded as information by the reconstruction algorithm. This work indicates that for a large attenuating medium there are notable differences between the four ways of including attenuation and scatter within the reconstruction - fully pre-correction of the data is inferior compared to all the other methods. For the case of simple shift-invariant Gaussian model of scatter - subtraction, additive and unified model methods shows similar variance-bias characteristics. Multiple realisations of simulated data sets have been used to compare the performance of this model with other methods.