A practical method of incorporating the randoms and scatter corrections into the system matrix of iterative PET reconstructions

Objectives Randoms and scatter corrections are essential and critically important for improving the contrast and quantitative accuracy in PET imaging. Iterative reconstruction algorithms have also been demonstrated to improve image quality. In this work, we describe a practical method of incorporating any existing randoms and scatter corrections into the system matrix of iterative PET reconstructions without increasing the matrix size.

Methods We compared the images reconstructed with our Practical Randoms and Scatter System Model (PRSSM) method to those reconstructed with the conventional Ordinary Poisson (OP) approach using contrast and resolution phantoms. The PRSSM method estimates the trues fraction within the prompts for each line-of-response using the variance reduced randoms, the single scatter simulation, and the acquired prompts. The trues fraction is then incorporated into the weighting component of the system matrix (i.e. the diagonal elements) similar to the attenuation correction weighting. The images were reconstructed using 3D-OSEM.

Results From the contrast and resolution vs noise and iteration, we have observed that the PRSSM method iterates towards (~5%) higher contrast values and converges faster as compared to the conventional OP method. Similar results were observed from the resolution measurements with the PRSSM method reaching a slightly higher resolution and noise at the same iteration. The reconstruction task was also observed to be up to 10% faster for the PRSSM method as there is no need to process through the randoms and scatter sinograms in the forward projection step for every iteration as compared to the OP method and the computation of the trues fraction is sufficiently fast.

Conclusions The preliminary results demonstrated that the PRSSM method can stop at an earlier iteration and achieve similar/higher contrast and resolution as compared to the conventional OP method with a faster reconstruction time. The PRSSM method needs to be further evaluated and optimized for various counting statistics