Bayesian Uncertainty Quantification and Regularized Reconstruction for CT-Based Dimensional Metrology

Statistical methods within the Bayesian framework have been widely used to address inverse imaging problems, such as computed tomography (CT) image reconstruction. These methods offer a probabilistic approach that is able to enhance the reconstruction quality by employing regularization methods while enabling uncertainty quantification of the result, providing valuable insights into the reliability of the reconstructed images. However, despite the flexibility and range of techniques within this framework, the computational intensity of this class of approaches is still impractical for large-scale datasets like those in CT. In this manuscript, we introduce a concept for determining the uncertainty caused by the noise in the observed data in CT-based dimensional measurement using a rapid, regularized, Markov Chain Monte Carlo reconstruction technique. This method provides a volumetric model where each voxel is represented by a distribution, which is then transformed into a triplet of gray value models: one for the central value and one each for the upper and lower bounds of the confidence interval. Bi-directional and uni-directional length measurements on results derived from each single-gray-value model, for real CT data, provide a task-specific measurement uncertainty. This method requires significantly less computation and storage capacity compared to classic Monte Carlo simulations by reducing the number of needed simulations for approximating a distribution while incorporating regularization techniques. The results are compared to conventional non-regularized and regularized reconstruction methods, such as Feldkamp-David-Kress (FDK), and state-of-the-art statistical methods, followed by validation of the determined uncertainty in real CT data.