Estimation of Statistical Weights for Model-Based Iterative CT Reconstruction

Since the introduction of model-based iterative reconstruction for computed tomography (CT) by Thibault et al. in 2007, statistical weights play an important role in the problem formulation with the objective to improve image quality. Statistical weights depend on the variance of measurements. However, this variance is not known and therefore weights must be estimated. So far, the literature neither discusses how statistical weights should be estimated nor how accurate the estimation needs to be. Our submission aims at filling this gap in the literature. Specifically, we propose an estimation procedure for statistical weights and assess this procedure with real CT data. The estimated weights are compared against (clinically unpractical) sample weights obtained from repeated scans. The results show that the estimation procedure delivers reliable results for the rays that pass through the scanned object. Four imaging scenarios are considered; in each case the root mean square difference between the estimated and sample weights is below 5% of the maximum statistical weight value. When used for reconstruction, these differences are seen to have little impact: all voxel values within soft tissue (low contrast) regions differ by less than 1 HU. Our results demonstrate that the statistical weights can be sufficiently well estimated to closely approach the result that would be obtained if the weights were known.