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Monte Carlo Reconstruction: a concept for propagating uncertainty in computed tomography

Published

Author(s)

Massimiliano Ferrucci, Evelina Ametova, Wim Dewulf

Abstract

We present a concept for propagating uncertainty in X-ray computed tomography (CT) by a Monte Carlo Reconstruction (MCR) technique, comprising repeated reconstructions with varying input parameters. The proposed technique follows the framework for model-based X-ray CT uncertainty assessment per the Monte Carlo Method (JCGM 101), although provides several advantages over the conventional implementation, which relies on simulating all individual steps in the X-ray CT measurement procedure and therefore considered to be impractical due to its high computational demand. The proposed method requires only a single set of simulated projections. For each Monte Carlo trial, the instrument geometrical parameters in a filtered back projection reconstruction algorithm are randomly sampled from specified uncertainty distributions. The output is a four-dimensional volumetric model where each voxel, defined by its three-dimensional indices, is represented by a distribution of reconstructed gray values. We reduce the four-dimensional volumetric model to three single-gray-value voxel models by calculating descriptive statistics: a voxel-wise lower gray confidence limit, a central gray value, and an upper gray value confidence limit. Dimensional measurements performed on the surfaces determined from each single-gray-value model provide insight on the effect of uncertainty in the instrument geometry. The proposed approach requires significantly less computations and data storage per Monte Carlo trial and provides a straight-forward way to relate uncertainties in reconstructed gray values to uncertainties in subsequent dimensional measurements. This, in turn, facilitates the practical application of the Monte Carlo Method in X-ray CT. We implement MCR to determine uncertainty distributions in the simulated X-ray CT measurement of a simple cube and an impeller due to uncertainties in the instrument geometry. Possible extension of MCR to other sources of uncertainty in the X-ray CT measurement process is discussed in the conclusions.
Citation
CIRP Journal of Manufacturing Science and Technology
Volume
32

Keywords

computed tomography, measurement uncertainty, geometrical calibration, probability distributions, Monte Carlo

Citation

Ferrucci, M. , Ametova, E. and Dewulf, W. (2021), Monte Carlo Reconstruction: a concept for propagating uncertainty in computed tomography, CIRP Journal of Manufacturing Science and Technology, [online], https://doi.org/10.1088/1361-6501/ac07db (Accessed April 22, 2024)
Created July 19, 2021, Updated December 9, 2022