Noise properties of four strategies for incorporation of scatter and attenuation information in PET reconstruction

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.