Maximum Likelihood Emission Image Reconstruction for Randoms-Precorrected PET Scans

Abstract

Most PET scans are compensated for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences. Real time subtraction of delayed coincidences compensates for the average of AC events, but also destroys the Poisson statistics. Moreover, negative values result during the real-time subtraction which would cause conventional penalized maximum likelihood algorithms to diverge, and setting these negative values to zero introduces a systematic positive bias. The authors have previously developed and compared two new methods for reconstructing transmission scans from randoms precorrected measurements: one based on a “shifted Poisson” (SP) model, and the other based on saddle-point (SD) approximations. Simulations and experimental phantom studies of transmission scans showed that both SP and SD methods lead to significantly lower variance than the conventional maximum likelihood methods (based on the ordinary Poisson (OF) model). The authors have now extended these methods to emission scans. In situations like 3D PET emission scans (with low counts per ray but many total counts and high randoms rates), they show that the proposed methods not only avoid the systematic positive bias of OP method but also lead to significantly lower variance. The new methods offer improved image reconstruction in PET through more realistic statistical modeling, yet with negligible increase in computation over the conventional OP method.