Statistical comparison of likelihood models for low dose x-ray CT

Iterative reconstruction in x-ray CT using maximum likelihood estimation (MLE) seeks to improve image quality over analytic techniques by accurately modeling the statistics of the CT acquisition. However there are a variety of statistical models to choose from, each providing a different tradeoff between data fidelity and computational simplicity. In this work, we simplify the reconstruction task to estimating the depth of a single stack of material, which makes estimation tractable for any model. We use this methodology to compare the tradeoffs of different statistical models. We specifically focus on comparing the added value in using complex, clinically infeasible models over conventional ones. The likelihood function for various statistical CT models is calculated either analytically or computationally for a particular x-ray source/detector system. Computational likelihoods are built through repeated calculation of their density functions. From these likelihoods, the bias and variance of each MLE are calculated. Excluding electronic noise, the bias and variance improvements of accurately modeling quantum noise with a compound Poisson model are negligible after accounting for beam hardening. Two strategies for including electronic noise - as additive Gaussian noise in the likelihood vs simple thresholding - are examined. Although each strategy leads to different estimates at low signals, their overall performance is similar. While accounting for beam-hardening of multi-energetic x-ray spectrum is important, we found that the benefit of modeling energy-integrating detectors is negligible. Also, while the presence of electronic noise worsens estimation performance at low signal levels, incorporating electronic noise in the likelihood model doesn't improve performance compared to thresholding.