An exact modeling of signal statistics in energy-integrating x-ray computed tomography

Energy-integrating detection of x-ray sources is widely used by modern computed tomography (CT) scanners and has been an interesting research topic for the purpose of more accurately processing the data toward low-dose applications. While the energy-integrating detection can be described by a compound Poisson distribution, this work provides an alternative means to explicitly consider the Poisson statistics of the quanta and the energy spectrum of the x-ray generation. An exact solution for the first two orders of the compound Poisson statistics is presented. Given the energy spectrum of an x-ray source, the mean and variance of the measurement at any count-density level can be computed strictly. This solution can provide a quantitative measure on the condition under which an assumption of employing the most commonly-used independent identical distribution (i.i.d.), such as Gamma, Gaussian, etc, would be valid. A comparison study was performed to estimate the introduced errors of variance by using these substitute statistical functions to approximate the actual photon spectrum. The presented approach would further be incorporated in an adaptive noise treatment method for low-dose CT applications.