Randoms Smoothing Based on Rates of Object Singles for CBM PET Scans

For quantitative PET, estimation of mean randoms from the measurement of delays relies on accurate estimate of the singles rates. For a continuous bed motion scan, the mean detector singles rates change constantly over time during the scan. The conventional formula based on detector singles rates involves averaging a nonlinear function of singles rates over time, which greatly increases the number of unknowns and the difficulty of estimation. In this work, a new formula for the CBM mean randoms was proposed, based on the object singles rates, which can be estimated by single-bed random smoothing algorithms. The object singles rates are singles rates measured by an ideal virtual scanner co-moving with the object and bed, reflecting the spatial distribution of singles rates within the object. Under approximations, a simplified approach was also derived, which requires no knowledge of the detector singles efficiencies, physical degrading factors, and acquisition parameters. Our method was evaluated by simulations on a Siemens next generation SiPM PET/CT prototype scanner with TOF mashing and by phantom measurements on a Siemens mCT PET/CT scanner. Unbiased estimations were obtained with much smaller variances than the raw delays. In conclusion, we developed a CBM randoms smoothing method which is based on the object randoms that can be estimated by the single-bed maximum likelihood algorithms. A simplified approach utilizes the fully 3D delays and leads to approximately unbiased estimates.