PET Energy-Based Scatter Estimation in the Presence of Randoms, and Image Reconstruction With Energy-Dependent Scatter and Randoms Corrections

In this paper, we address the problem of energy-based scatter estimation in PET in the presence of randoms. We refine a previous proposed model for comprehensive use of the energy information in PET [Phys. Med. Biol., vol. 51, pp. 2919-2937, 2006] by introducing a model for the random coincidences. This model is used to estimate the scatter components in randoms from delayed coincidence data, and then of the nonrandom coincidence scatters from the prompt coincidence data. By performing these estimations on a spatial grid covering the data space, we obtain scatter and randoms correction terms that depend both on position and energy. These terms are incorporated into the list-mode image reconstruction algorithm, thus allowing for an individual treatment of each event according to its position and energy information. We test this approach by using a recently developed image quality evaluation procedure that measures the detectability of signals at unknown locations. The procedure combines a three-dimensional image scanning technique with a novel nonparametric free-response data analysis method that provides a signal detectability metric by using an exponential transformation of the free-response operating characteristic (EFROC). The method allows for scaling of the detectability index to any given image size, a property that makes it advantageous for application to phantom experiments with multiple signals, or large background volumes that can be scanned for false signals. Such experiments can provide substantial signal detectability information with only a few images, as we show here. Image reconstructions using traditional, no energy-dependent, and energy-dependent corrections are compared for different time-of-flight (TOF) resolutions, and number of counts. A comparison of PET time-of-flight (TOF) performance versus no-TOF is also presented.