Maximum likelihood estimation of detector efficiencies in positron emission tomography

In this paper, we introduce a maximum-likelihood (ML) method for estimating detector efficiencies; in positron emission tomography. First, we develop a Poisson model for blank scan data obtained from rotating rod sources. Then, we estimate the detector efficiencies using two expectation-maximization (EM) algorithms that differ in the way the maximization step is solved. As desired, the resulting algorithms have the property that the log-likelihood function is non-decreasing as the iteration number increases. Simulation studies using synthetic data demonstrate that the proposed algorithms outperformed two alternative approaches.