An evaluation of image noise variance for time-of-flight PET

We describe a simple theoretical framework for linear time-of-flight (TOF) reconstruction and evaluate several alternative TOF filters. We implement a capability for direct computation of TOF noise variance images and evaluate the gain in image variance for TOF vs. non-TOF for 1.26 nsec TOF resolution on the Siemens biograph HiRez PET/CT. The variance calculation is validated by comparing to pixel variances computed from replicated synthetic data. TOF reconstruction does not give a uniform improvement in image noise variance, but improves variance more toward the periphery of an object than at its center. The TOF performance gain depends on how random coincidences are processed, and is greater when the randoms fraction is higher, or when randoms smoothing is not employed. We confirm that TOF gain is greater for larger objects than for smaller ones, but find discrepancies with the D/Delta x rule of thumb. With 1.26 nsec resolution on the HiRez, TOF image noise gain factors (non-TOF/TOF variance) range from 1.5 to 2.2 on the measured data at hand. We predict that an improvement in TOF resolution by a factor of 2 (to 600 psec) could improve image variance on this machine by an additional factor of 1.8. We find that confidence weighted TOF reconstruction under-performs non-TOF reconstruction for objects whose diameters are small compared to the TOF resolution.