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

Abstract

We present a concept for propagating uncertainty in x-ray computed tomography (CT) using 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 it provides several advantages over the conventional implementation, which relies on simulating all individual steps in the x-ray CT measurement procedure and is 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 value confidence limit, a central gray value, and an upper gray value confidence limit. Bi-directional length measurements performed on the surfaces determined from each single-gray-value model provide insight into the effect of uncertainty in the instrument geometry. The proposed approach requires significantly fewer computations and data storage per Monte Carlo trial and provides a straightforward 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.