Estimation of uncertainty in respiratory-gated PET images

Positron Emission Tomography (PET) is a powerful tool for patient diagnosis and assessment of therapy response, which is carried out through comparison of PET measurements from longitudinal scans. However, as with any measurement tool, an estimate of error or uncertainty is required for meaningful comparison of such measurements. We have developed a bootstrap-based method for estimating uncertainty in respiratory-gated PET images. First, we independently reconstruct a set of gated images, each corresponding to a different stage in the respiratory cycle. We then apply a Bayesian framework to estimate parameters of the underlying posterior probability distribution of radioactivity concentration at each voxel, using a Gaussian model with non-negative mean, and considering the variance of the Gaussian model as a nuisance parameter with an asymptotically locally invariant prior. Once the posterior distribution of the radioactivity concentration at each voxel is determined, relevant image statistics are obtained at each voxel, either in closed-form (for the mean and standard deviation), or through numerical methods (for confidence intervals). The mean of the estimated distribution is shown to be a quantitatively better image than that obtained by averaging the set of gated reconstructions, yielding tighter confidence intervals for the values measured at each voxel. The procedure was successfully tested on real PET data.