Comparison of two motion compensation models: Adding ordered subset into the mix

The motion compensation model was introduced to improve statistical accuracy of iterative tomographic image reconstruction in the presence of periodic motion. However, this is achieved at the expense of substantial extra computational burden to handle all gated histograms simultaneously. An alternative model was proposed by re-interpreting the interdependence of the Poisson processes defining the projection data along the motion axis, thus allowing all gated histograms to be merged into a single one for reconstruction. It was demonstrated that much less computational resources were then required to converge using this Merged model, while achieving equivalent image quality. In this work, we investigate the impact of Ordered Subsets (OS) on the convergence rate and image quality of the Merged model compared to the Classical motion compensated model. Comparison of 1, 2, 4 and 8 OS was performed using simulated and experimental datasets. As expected, the gain in convergence rate was roughly proportional to the number of OS for both models and both datasets. Both models also converged to images that were equally well correlated to the ground truth. However, the Merged model was observed to retain its advantage in computational resources over the Classical model, which amounted to a three fold gain for our experimental dataset. In conclusion, the proposed Merged model is a promising approach for imaging applications involving periodic motion, such as cardiac or respiratory gated studies.