Evaluation of the accuracy of CT numbers in statistical correction of nonlinearity for polychromatic X-ray CT projection data

Abstract

The CT number is theoretically independent of the number of incident photons and the thickness of a subject. However, when noise is added, the CT number becomes dependent on the number of incident photons because of the nonlinearity of the logarithm operation, and so the accuracy of the CT number is degraded, especially in a photon-starved state. The inconsistency of the CT number due to nonlinearity generates an intense streak artifact in a reconstructed image. We have theoretically clarified the statistical characteristics of both the nonlinearity of the logarithm transform and the non-zero/non-negative restriction in the logarithm operation. Moreover, we have formulated a correction method for such nonlinearity according to the statistical distribution of noise, and we carried out computer simulations for monochromatic X-ray beams. However, the applicability to polychromatic-energy photons has not been confirmed. The artifacts induced by the beam-hardening effect, which occurs when incident beams are polychromatic, remarkably deteriorate the accuracy of the CT number. In this paper, we quantitatively evaluate the improvement of the quality of reconstructed images by our correction method by using a numerical experiment when incident beams are polychromatic. The experimental results show that there is less influence on spatial resolution and that the CT number is hardly dependent on the number of incident photons for a polychromatic beam as well as a monochromatic beam. Moreover, the results suggest the possibility that the same image quality is obtained at a much lower exposure level than the clinical exposure level of low-dose CT.