Construction of a Nearly Unbiased Statistical Estimator of Sinogram to Address CT Number Bias Issues in Low-Dose Photon Counting CT

Photon counting detector (PCD)-CT has demonstrated promise to reduce ionizing radiation exposure further and improve spatial resolution. However, when the radiation exposure or the detector pixel size is reduced, image noise is elevated, and the CT number becomes more inaccurate. This exposure level-dependent CT number inaccuracy is referred to as statistical bias. The issue of CT number statistical bias is rooted in the stochastic nature of the detected photon number, N, and a log transformation used to generate the sinogram projection data. Due to the nonlinear nature of the log transform, the statistical mean of the log-transformed data is different from the desired sinogram, the log transform of the statistical mean of N. Consequently, when a single instance of N is measured, as in clinical imaging, the log-transform leads to an inaccurate sinogram and statistically biased CT numbers after reconstruction. This work presents a nearly unbiased and closed-form statistical estimator of sinogram as a simple yet highly effective method to address the statistical bias issue in PCD-CT. Experimental results validated that the proposed approach addresses the CT number bias problem and improves the quantification accuracy of both non-spectral and spectral PCD-CT images. Additionally, the process can slightly reduce noise without adaptive filtering or iterative reconstruction.