Statistical decision making in emission tomography using emission-count posteriors

We present a new approach to decision making based on the concept of emission counts (EC), i.e., the number of events emitted per voxel during the scan. The approach allows direct computation of posterior probabilities of hypotheses defined in terms of EC, and is applicable to any type of emission tomographic list-mode projection data, e.g., SPECT, PET, or time-of-flight (TOF)-PET, as well as binned data which can be considered a special case of list-mode data. Conditional Bayesian (CB) decision theory utilizing values of the posterior probability of hypotheses as test statistics are used to derive decision rules. We demonstrate that the derived decision principle is equivalent to the likelihood-ratio ideal observer for binary hypothesis testing. We use data acquired in list-mode format for an anthropomorphic torso phantom using a lanthanum-bromide time-of-flight PET scanner to provide examples of application of EC-CB observer. For data-specific decisions, we demonstrate examples of multiple-hypotheses decision making. For imaging system evaluation, we define two regions of interest (ROIs) on the image, and two hypotheses, H₁ and H₂, that one ROI emitted on average at least r times more events than the other region. The posterior probabilities of H₁ and H ₂ are determined. ROC curves are constructed using 50 projection data sets (list-mode files), each including 16 million prompts, from which 25 data sets correspond to H₁ and the other 25 to H₂. The areas and partial areas under the ROC curves are used as figures of merit evaluating the performance of the LaBr₃ PET system in discriminating between H₁ and H₂ with and without TOF information. Summary: A new optimal numerical observer which makes decisions based on posterior probability of emission counts is presented. The utility of the observer for hypothesis testing is demonstrated on TOF list-mode phantom data acquired on PENN LaPET scanner.