The Influence of Photon Counting Statistics on Picture Noise and Reproducibility in Quantitative Computed Tomography

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Abstract
Photon noise in the projection data of CT-measurements causes picture noise in the reconstructed images. This noise limits the precision of quantitative parameters such as for example the mean CT-value within a region of interest (ROI). The precision of this parameter is usually estimated as the standard error of the mean (SEMpix) calculated from the root mean square deviation of the pixel values within the ROI. The reproducibility of the mean value (SEMrep) however is limited by the photon statistics in the projection data and can be determined from repeated measurements as the root mean square deviation of the mean ROI values. The reconstruction process correlates individual picture elements, therefore SEMpix and SEMrep are not identical. Using the linearity of the convolution backprojection reconstruction algorithm, we present a new linear vector space notation and derive the relation between photon noise in the measured projection data and reproducibility of the mean CT-value in arbitrarily shaped ROIs. An easy to implement formula enables the calculation of the reproducibility, even if the tissue distribution in the ROI is not homogeneous. CT data from a special purpose low dose X-ray CT scanner were used to document the validity of our results for actual measurements. In addition the theoretical results and those from actual measurements of a comparison between SEMpix and SEMrep for the special case of circular ROIs with homogeneous material distribution are given.