Comparison between pre-log and post-log statistical models in low-dose CT iterative reconstruction

X-ray detectors in clinical computed tomography (CT) operate in energy-integrating mode. Their signal statistics is complicated by a cascade of random processes which prevent a highly accurate model of signal statistics from being practical for CT iterative reconstruction algorithms. Since all models are approximations, it is natural to ask whether incremental refinement of their accuracy may be beneficial in practice. In the design of CT model-based iterative reconstruction (MBIR), pre-log and post-log models are the two major categories of statistical models being considered, but it is rather uncertain whether one model could lead to notably improved image quality over the other in realistic situations. In this study, we compare pre-log and post-log MBIR methods using real phantom data acquired on a GE Discovery CT750 HD system over a wide range of x-ray dose levels. The pre-log MBIR included Beer's law, beam-hardening effects, and all major data calibration factors in a nonlinear forward model to perform three-dimensional image reconstruction directly from raw multi-slice CT measurements, whereas the post-log MBIR used pre-corrected and log-converted data so that a simpler linear forward model was used. We found that pre-log MBIR achieved better CT number accuracy in low dose settings when compared to post-log MBIR, but the two methods produced very similar images at high and medium dose settings. Although a few potentially attractive options remain to be explored to further improve the image quality of both pre-log and post-log methods, we conclude that accurate noise models may be important for iterative reconstruction of very low dose CT datasets, and careful design and optimization of the models should not be overlooked in the design of CT MBIR.