Principle Analysis for the Possibility of Scattered X-Ray to Improve Computed Tomography Reconstruction

If scattered X-rays carry information that is independent of that is carried by primary X-rays, the accuracy of attenuation coefficients estimated using both primary and scattered X-rays is expected to be better than that estimated using only primary X-rays. However, because scattered X-rays cannot be easily introduced into conventional X-ray computed tomography (CT), the issue has gained scant attention. This study demonstrates theoretically that the measurement of scattered X-rays improves the accuracy of reconstruction in CT, even in a photoelectric absorption scenario. Here, the CT geometry was simplified for a system that targeted a homogeneous thin cylinder, retaining the necessary configuration. Furthermore, we constructed a mathematical model termed the π-junction model. This model is an extension of the T-junction model used in one of our previous studies. It addresses the photoelectric effect, which was not considered in the T-junction model. The variance in the estimation of the attenuation coefficients of this model from the measurements of both primary and scattered photons was evaluated as the Cramer-Rao lower bound. Both the theory and numerical experiments using Monte Carlo simulation showed that the accuracy of estimating the attenuation coefficient could be improved by measuring the scattered X-rays together with the primary X-rays, even in the presence of photoelectric absorption. This result provides a basis for the superiority of using scattered X-rays.