Signal statistics of x-ray computed tomography

Probability distribution functions (pdf's) of x-ray computed tomography (CT) signals form the basis for statistical reconstruction algorithms and for noise-simulation experiments. The conventional model for pdf's assumes a quanta-counting process obeying a discrete Poisson distribution. In reality, CT scanners employ energy-integrating sensors detecting a polyenergetic X-ray beam, with data quantized for digital reconstructions. A model was developed for the CT signal consisting of an energy spectrum of x-ray quanta (individually obeying Poisson statistics), contributing an incremental signal, proportional to their energy, to an analog-to-digital converter. Using a moment generating function approach, the pdf is shown to be a Compound Poisson process that is functionally dependent on the x-ray energy spectrum, flux level, and quantization step size. Pdf's were computed numerically by a Fourier transform of the characteristic function and compared to experimental pdf's collected from phantom scans. For exposures encountered in normal clinical usage, the pdf is similar to the conventional Gaussian approximation, with rescaling for quantization and polyenergetic spectra. For low intensities, the deviation from the conventional photon-counting (Poisson) model is significant and may have implications for statistical reconstruction algorithms.