Noise Properties of Four Strategies for Incorporation of Scatter and Attenuation Information in PET Reconstruction Using the EM-ML Algorithm

Conventional methods for dealing with attenuation and scatter in PET can limit the reconstructed image quality, particularly if the attenuating medium is large (as in whole body 3D PET). In such cases, often a substantial scatter subtraction is performed followed by amplification of the remaining data (to correct for attenuation) resulting in noisy reconstructions. More recent iterative reconstruction methods 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 of including attenuation and scatter to the case where attenuation and scatter information are both included within the system matrix used by the expectation maximization maximum likelihood (EM-ML) algorithm. For this case all acquired data are used and regarded as a source of information by the reconstruction algorithm. Multiple realisations of simulated data sets have been used to compare the performance of the unified attenuation and scatter model with other methods. For a large attenuating medium and low counts there are notable differences between the four main ways of including attenuation and scatter within the reconstruction-with full pre-correction of the data being inferior compared to all the other methods, and the method which models scatter and attenuation within the system matrix showing some advantages. This work suggests that if regularisation of the EM algorithm is carried out by early termination of the iterative process, the subtraction method is the better approach among the techniques considered. In contrast, if a post-reconstruction smoothing approach to regularisation is to be used (whereby highly iterated, noisy image estimates are smoothed), the full modeling method for attenuation and scatter yields the better results, albeit at the computational cost of many more iterations being required