VARIANCE APPROXIMATION FOR EXPONENTIAL FAMILY PENALIZED MAXIMUM LIKELIHOOD ESTIMATORS: APPLICATION TO KINETIC PARAMETRIC ESTIMATION

We further simplify previously published general approximate expressions for the covariance of penalized maximum likelihood estimators for likelihoods with the canonical form of the exponential family. The resulting expression makes calculation of the covariance more tractable for cases involving complicated log-likelihood expressions. We use this approximation to derive the covariance of direct estimates of voxel-wise kinetic parameters from list mode and bin mode PET data. To evaluate the accuracy of the approximation we simulate a simple parametric image reconstruction problem and demonstrate that the approximate covariances match well with the empirical covariances.