EM reconstruction with multiple time dependences

Cardiac ⁸²Rb PET can have a high initial count rate due to the short halflife of ⁸²Rb. This high count rate can result in an initially high randoms rate and substantial deadtime. With the short halflife, the deadtime and randoms fractions change dramatically over the duration of the scan. Accounting for this time dependence for more accurate reconstruction is the goal of this study. In particular, an expectation-maximization (EM) algorithm was developed to exploit differences between true, scattered, and random events over the time course of the scan and also to exploit differences in time-of-flight (TOF) information. The algorithm can be expressed in terms of modulation functions that impact the expected true, scatter, and random events independently. These functions can also include the effect of deadtime on each contribution. When the modulation functions for the different components are equal, the update formulas revert to the standard EM solutions. The TOF dependence is accounted for as an independent dimension in the likelihood function; the trues follow a Gaussian distribution about the expected mean and the randoms follow a uniform distribution related to the timing-coincidence window. The formulas were tested by simulated list-mode data from a cardiac scan with cold defects. Three data sets were generated: trues-only (ideal data); trues and randoms; and trues and randoms with deadtime modeling. Reconstructions were performed using and not using TOF information.