Temporal Resolution Properties of Dynamic PET Reconstructions

We describe methods for computing mean and variance approximations to instantaneous and average rate estimates obtained from continuous-time penalized ML dynamic PET image reconstructions. The derivation is based on writing the likelihood for the list-mode data as the limiting case of the likelihood for binned sinogram data as the temporal bin width goes to zero. We show that approximations of the mean and covariance can then be computed for continuous-time penalized ML estimates by exploiting spatio-temporal separability and the use of Kronecker decompositions. The resulting expressions are tractible forms that provide estimates of the mean and of instantaneous and time-averaged covariance between any two voxels and time instances.