University of Oulu

Suuronen, J., Emzir, M., Lasanen, S., Särkkä, S., & Roininen, L. (2020). Enhancing industrial X-ray tomography by data-centric statistical methods. Data-Centric Engineering, 1, E10. doi:10.1017/dce.2020.10

Enhancing industrial X-ray tomography by data-centric statistical methods

Saved in:
Author: Suuronen, Jarkko1; Emzir, Muhammad2; Lasanen, Sari3;
Organizations: 1School of Engineering Science, Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
2Department of Electrical Engineering and Automation, Aalto University, Aalto, Finland
3Sodankylä Geophysical Observatory, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.3 MB)
Persistent link:
Language: English
Published: Cambridge University Press, 2020
Publish Date: 2021-02-10


X-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, as well as chemical, biomedical, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography reconstruction. In Bayesian methods, the inverse problem of tomographic reconstruction is solved with the help of a statistical prior distribution which encodes the possible internal structures by assigning probabilities for smoothness and edge distribution of the object. We compare Gaussian random field priors, that favor smoothness, to non-Gaussian total variation (TV), Besov, and Cauchy priors which promote sharp edges and high- and low-contrast areas in the object. We also present computational schemes for solving the resulting high-dimensional Bayesian inverse problem with 100,000–1,000,000 unknowns. We study the applicability of a no-U-turn variant of Hamiltonian Monte Carlo (HMC) methods and of a more classical adaptive Metropolis-within-Gibbs (MwG) algorithm to enable full uncertainty quantification of the reconstructions. We use maximum a posteriori (MAP) estimates with limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) optimization algorithm. As the first industrial application, we consider sawmill industry X-ray log tomography. The logs have knots, rotten parts, and even possibly metallic pieces, making them good examples for non-Gaussian priors. Secondly, we study drill-core rock sample tomography, an example from oil and gas industry. In that case, we compare the priors without uncertainty quantification. We show that Cauchy priors produce smaller number of artefacts than other choices, especially with sparse high-noise measurements, and choosing HMC enables systematic uncertainty quantification, provided that the posterior is not pathologically multimodal or heavy-tailed.

see all

Series: Data-centric engineering
ISSN: 2632-6736
ISSN-E: 2632-6736
ISSN-L: 2632-6736
Volume: 1
Article number: e10
DOI: 10.1017/dce.2020.10
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This work has been funded by Academy of Finland (project numbers 326240, 326341, 314474, 321900,313708) and by European Regional Development Fund (ARKS project A74305).
Copyright information: © The Author(s), 2020. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.