Accurate dynamic FIM estimation from list-mode PET data for uniform resolution reconstructions

The Fisher Information Matrix (FIM) plays a key role in the analysis and application of statistical list-mode image reconstruction methods based on inhomogeneous Poisson process data models. The dynamic PET FIM is derived by viewing list-mode data as the limiting case of bin-mode data as the bin-widths approach zero. The Generalized Error Lookup Table (GELT) method developed for the estimation of the FIM from static PET data is extended to estimate the dynamic PET FIM from list-mode data. GEET is a data plug-in technique for estimating reciprocals of mean counts at detector pairs and trades off variance to provide low bias reciprocal mean estimates that are in turn used to compute the FIM. GELT provides accurate FIM estimates even for low count datasets and is therefore particularly suitable for FIM estimation from list-mode data since most spatiotemporal data bins contain only a few counts. As an application, we present simulation results in which the diagonal entries of the dynamic FIM are used to modulate the spatiotemporal smoothing to achieve approximately uniform spatial resolution that remains constant over time.