Properties of preprocessed sinogram data in x-ray computed tomography

Abstract

The accurate determination of x-ray signal properties is important to several computed tomography (CT) research and development areas, notably for statistical reconstruction algorithms and dose-reduction simulation. The most commonly used model of CT signal formation, assuming monoenergetic x-ray sources with quantum counting detectors obeying simple Poisson statistics, does not reflect the actual physics of CT acquisition. This paper describes a more accurate model, taking into account the energy-integrating detection process, nonuniform flux profiles, and data-conditioning processes. Methods are developed to experimentally measure and theoretically calculate statistical distributions, as well as techniques to analyze CT signal properties. Results indicate the limitations of current models and suggest improvements for the description of CT signal properties.

An experimental study on the noise properties of x-ray CT sinogram data in Radon space

“…The convolution operation may alter the Poisson distribution (Snyder et al 1991). Additional calibration operations including the logarithm transform can further alter the Poisson distribution (Lu et al 2001, Whiting et al 2006. The data mean remains unaltered, however, the variance changes noticeably as the noise propagates through these calibration operations (Lu et al 2001, 2002, Li et al 2004, Whiting et al 2006.…”

“…Consider the polyenergetic nature of X-ray generation where the Poisson function becomes a compound Poisson form which includes a convolution with the X-ray energy spectrum (Snyder et al 1991, Whiting et al 2006. The convolution operation may alter the Poisson distribution (Snyder et al 1991).…”

“…Additional calibration operations including the logarithm transform can further alter the Poisson distribution (Lu et al 2001, Whiting et al 2006. The data mean remains unaltered, however, the variance changes noticeably as the noise propagates through these calibration operations (Lu et al 2001, 2002, Li et al 2004, Whiting et al 2006. In the following, we will focus on the mean-variance relationship of the Poisson distribution of the transmitted data in Radon space and present a modified mean-variance functional formula which accommodates the variance variation due to the preprocessing calibration operations and other factors, such as bowtie attenuating filtration.…”

“…To reconstruct an acceptable quality image, the transmitted data must be calibrated. While most of the calibration operations are system specific, a mathematical logarithm transform which converts the transmitted data into Radon space is common to all CT systems (Macovski 1982, Whiting et al 2006. Hereafter, the system calibrated and logarithm transformed data is referred to as the preprocessed sinogram or simply sinogram.…”

“…The detected counts reflect the transmitted X-ray photon numbers and their energies. Studying the noise properties of the transmitted data is currently an attractive research topic (Whiting et al 2006). To reconstruct an acceptable quality image, the transmitted data must be calibrated.…”