Relaxed ordered subset preconditioned alternating projection algorithm for PET reconstruction with automated penalty weight selection

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Performance of the preconditioned alternating projection algorithm (PAPA) using relaxed ordered subsets (ROS) with a non-smooth penalty function was investigated in positron emission tomography (PET). A higher order total variation (HOTV) regularizer was applied and a method for unsupervised selection of penalty weights based on the measured data is introduced.


A ROS version of PAPA with HOTV penalty (ROS-HOTV-PAPA) for PET image reconstruction was developed and implemented. Two-dimensional PET data were simulated using two synthetic phantoms (geometric and brain) in geometry similar to GE D690/710 PET/CT with uniform attenuation, and realistic scatter (25%) and randoms (25%). Three count levels (high/medium/low) corresponding to mean information densities (Symbols) of 125, 25, and 5 noise equivalent counts (NEC) per support voxel were reconstructed using ROS-HOTV-PAPA. The patients' brain and whole body PET data were acquired at similar Symbols on GE D690 PET/CT with time-of-fight and were reconstructed using ROS-HOTV-PAPA and available clinical ordered-subset expectation-maximization (OSEM) algorithms.


A power-law model of the penalty weights' dependence on Symbol was semi-empirically derived. Its parameters were elucidated from the data and used for unsupervised selection of the penalty weights within a reduced search space. The resulting image quality was evaluated qualitatively, including reduction of staircase artifacts, image noise, spatial resolution and contrast, and quantitatively using root mean squared error (RMSE) as a global metric. The convergence rates were also investigated.


ROS-HOTV-PAPA converged rapidly, in comparison to non-ROS-HOTV-PAPA, with no evidence of limit cycle behavior. The reconstructed image quality was superior to optimally post-filtered OSEM reconstruction in terms of noise, spatial resolution, and contrast. Staircase artifacts were not observed. Images of the measured phantom reconstructed using ROS-HOTV-PAPA showed reductions in RMSE of 5%–44% as compared with optimized OSEM. The greatest improvement occurred in the lowest count images. Further, ROS-HOTV-PAPA reconstructions produced images with RMSE similar to images reconstructed using optimally post-filtered OSEM but at one-quarter the NEC.


Acceleration of HOTV-PAPA was achieved using ROS. This was accompanied by an improved RMSE metric and perceptual image quality that were both superior to that obtained with either clinical or optimized OSEM. This may allow up to a four-fold reduction of the radiation dose to the patients in a PET study, as compared with current clinical practice. The proposed unsupervised parameter selection method provided useful estimates of the penalty weights for the selected phantoms' and patients' PET studies. In sum, the outcomes of this research indicate that ROS-HOTV-PAPA is an appropriate candidate for clinical applications and warrants further research.

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