Reconstruction-reprojection processing of transmission scans and the variance of PET images

Two methods for processing noisy transmission sinograms are compared on the basis of the sample variances of emission images reconstructed from simulated data. The first method, reconstruction-reprojection, reconstructs a transmission image and then reprojects and exponentiates it to form a smoothed set of attenuation correction factors. The other method low-pass filters each projection in the transmission data. Reconstruction-reprojection significantly reduces the variance of the attenuation correction factors even when the reconstruction step uses a ramp filter. Simulations were done to determine whether this reduction translates into a lower variance for the reconstructed emission image compared to low-pass filtering. A 20-cm cylinder was simulated for transmission sinograms with 0.5, 1, and 5 million counts. Emission sinograms were noiseless. Transmission sinograms were processed using Hanning filters with cutoff frequencies of 15%, 25%, 50%, and 100% of the Nyquist rate as well as a ramp filter. For high count conditions, reconstruction-reprojection processing reduced attenuation correction factor variances by a factor of 2.44 compared to low-pass filtering. However, the image variances obtained with both methods were not significantly different.<>