Non-Positive Corrections and Variance Models for Iterative Post-Log Reconstruction of Extremely Low-Dose CT Data

In extremely low-dose protocols to reduce radiation dose to patients, computed tomography (CT) images suffer from increased bias and low signal-to-noise ratio in measurements. In this study, we consider three different non-positive corrections, flip, truncation and mean-preserving filter (MPF), affecting the measurement mean, propose a new variance expression for weights in weighted least-squares (WLS) reconstruction, and evaluate the impact on changes in the mean and variance of measurements. We simulated 1000 polychromatic CT sinograms of a chest phantom, including realistic levels of quantum and electronic noises. For the simulated scenario of 80 kVp and 0.5 mAs, compared to the conventional threshold and flip methods, the mean-preserving filter reduced the bias in post-log sinogram values by up to five times. Simple weights in WLS reconstruction that neglected the effect of non-positive correction limited improvements in the image quality. The advanced variance estimates considering electronic noise and the effect of pre-processing on the variance change made both WLS and penalized WLS reconstructions improve. Although the image quality improvement from a WLS reconstruction based on a Gaussian post-log distribution is inherently limited, the proposed method for estimating the post-log variance including electronic noise and the effect of pre-corrections from a single measurement leads to some improvements in variance estimates for post-log CT data and showed the feasibility of post-log iterative reconstruction for extremely low-dose CT imaging.