Statistical approach to X-ray CT imaging and its applications in image analysis. I. Statistical analysis of X-ray CT imaging.

A statistical description of X-ray CT (computerized tomography) imaging, from the projection data to the reconstructed image, is presented. The Gaussianity of the pixel image generated by the convolution (image reconstruction) algorithm is justified. The conditions for two pixel images to be statistically independent (for a given probability) and the conditions for a group of pixel images to be a spatial stationary random process and ergodic in mean and autocorrelations are derived. These properties provide the basis for establishing the stochastic image model and conducting the statistical image analysis of X-ray CT images.