Objective assessment of image quality. V. Photon-counting detectors and list-mode data

A theoretical framework for detection or discrimination tasks with list-mode data is developed. The object and imaging system are rigorously modeled via three random mechanisms: randomness of the object being imaged, randomness in the attribute vectors, and, finally, randomness in the attribute vector estimates due to noise in the detector outputs. By considering the list-mode data themselves, the theory developed in this paper yields a manageable expression for the likelihood of the list-mode data given the object being imaged. This, in turn, leads to an expression for the optimal Bayesian discriminant. Figures of merit for detection tasks via the ideal and optimal linear observers are derived. A concrete example discusses detection performance of the optimal linear observer for the case of a known signal buried in a random lumpy background.