Maximum likelihood estimation of detector efficiencies for positron emission tomography

Positron emission tomography (PET) is a medical imaging modality that enables physicians and researchers to study biochemical process within the human body and small animals. In PET, a subject is administered a radiopharmaceutical that is absorbed preferentially by the region-of-interest (e.g., brain). Due to the radiopharmaceutical and certain interactions at the cellular level, photon pairs are emitted in all directions and the number of photon pairs emitted from a region is proportional to the metabolic rate of the region. PET scanners are designed to detect and count the photon pairs. From this photon count data, images are reconstructed whereby the value of a pixel is proportional to the metabolic rate of the region associated with the pixel. The reconstructed images provide valuable information to help physicians detect abnormalities, such as tumors, which have extremely high metabolic rates.; There are many sources of error in PET that must be addressed in order to obtain accurate images. The focus of this research is the problem of detector inefficiency. Due to inherent detector non-uniformity, detector efficiencies are less than 100%. To obtain more precise emission images, the photon count data must be corrected to account for the effect of detector inefficiency.; We introduce a maximum-likelihood method for estimating detector efficiencies in PET. First, we develop three Poisson models for blank scan data obtained from rotating rod sources. Then, for each model, we estimate the detector efficiencies using expectation-maximization algorithms, where the maximization step is solved using two optimization algorithms. As desired, the resulting algorithms have the property that the log-likelihood function is non-decreasing as the iteration number increases. For each data model, one of the proposed algorithms guarantees that the efficiency estimates always lie in the interval [0, 1]. Although the second algorithm for each data model does not have this property, in all of the experiments performed it produced efficiency estimates that were between zero and one. Simulation studies using synthetic data demonstrate that, based on various comparison criteria, the proposed estimation algorithms outperform two alternative approaches. Additionally, simulation studies using real data show that the third Poisson model leads to much better reconstructed emission images than the first two models.