Prior modelling and uncertainty quantification in X-ray computed tomography with application to defect detection in subsea pipes

X-ray computed tomography (CT) is a widely used imaging modality for instance in medical examination, airport security, and nondestructive testing in industry. The technology involves measuring Xray attenuation through an object from many angles and using that data to reconstruct a cross-sectional image representing the hidden interior of the object. This makes CT a classical inverse problem, where indirect measurements are used to infer information about hidden parameters. It is key to realize that the CT reconstruction is not an image of reality but a representation that depends on data quality and a mathematical model. CT imaging is subject to several sources of error and uncertainty that can lead to deviations between the reconstruction and reality, including: data noise, incomplete data, model approximations, model error, and discretization error. Therefore, it is relevant to pose the CT reconstruction problem in a Bayesian paradigm, where uncertainties are quantified and propagated into the solution.

One of the main topics of this PhD thesis concerns prior modelling for Bayesian CT. In the Bayesian approach, a priori (preceding) knowledge,beyond the measured data, can be introduced as a prior probability distribution that is used to inform the CT reconstruction. This is particularly relevant when the measured data is incomplete. Prior modelling depends on the application at hand, and in this thesis, CT inspection of subsea pipes for defect detection is used as a case study. A priori knowledge about subsea pipes regards their approximate internal layered structure as well as which materials they consist of.The challenge is to translate this information into mathematical formulations of probability distributions that can be incorporated in the Bayesian CT problem. Contributions of this thesis include two approachesto modelling this a priori information: a structural Gaussian prior and parameterizing pipes via simple geometric shapes. Furthermore,contributions include a reconstruction method with built-insegmentation of defects, which was enabled by significantly different priors for pipe and defect structures. In addition, this thesis considers uncertainty quantification for CT inspection of pipes and provides uncertainty estimates related to reconstructions, which might aid indecision making regarding pipe integrity.

The work carried out for this PhD project also includes major contributions to a general Python package for computational Bayesian inverse problems and uncertainty quantification (CUQIpy). This package contains a suite of probability distributions, models, samplers, analysis tools, and plotting tools, and it can be combined with the users own code if needed. With CUQIpy, the user can specify and solve their particular Bayesian inverse problem using just a few lines of Python code. Furthermore, the PhD work concerns major contributions to an accompanying plugin (CUQIpy-CIL) that creates an interface between CUQIpy and a third party library for CT reconstruction. CUQIpy-CIL provides a simple computational platform for Bayesian CT reconstruction and uncertainty quantification.