Analysis of Statistical Models for Iterative Reconstruction of Extremely Low-Dose CT Data

In order to reduce CT radiation dose, there have been numerous efforts to develop low-dose acquisition protocols as well as noise reduction methods such as data denoising and iterative reconstruction. In this study, we analyze the first and second order statistics of post-log CT data and the resulting impact on iterative image reconstruction for extremely low-dose CT acquisitions. We performed a CT simulation incorporating polychromatic forward projection and realistic levels of quantum and electronic noise. We performed N=1000 simulations of a chest phantom to analyze the impact of processing steps on the statistics of post-log data. We investigated the impact of two non-positivity correction methods, threshold and mean-preserving filter. And, we analyzed the bias and variance of different weighting terms and performed weighted least squares reconstruction with these different weights. For the simulation of an extremely low dose chest acquisition with 80 kVp and 0.5 mAs, the mean-preserving filter reduced the mean bias of post-log sinogram by roughly seven times compared to the threshold method. The WLS reconstructed images using simple weighting terms that ignored the effect of non-positive correction lead to limited improvements in image quality. Accurate weighting terms including electronic noise and the variance change from MPF provided superior images, especially in highly attenuating regions where bias reductions of similar to 17% were achieved compared to simple weighting matrices. Appropriate selection of the non-positivity correction method is essential for low flux CT data processing. The proposed method for estimating the weighting matrix with electronic noise and the effect of pre-corrections leads to some improvements in variance estimation for post-log CT data, although it has potential for further improvement.