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

IF 2.4 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE DataCentric Engineering Pub Date : 2020-03-08 DOI:10.1017/dce.2020.10
Jarkko Suuronen, M. Emzir, Sari Lasanen, S. Särkkä, L. Roininen
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引用次数: 7

Abstract

Abstract 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. Impact Statement Industrial X-ray tomography reconstruction accuracy depends on various factors, like the equipment, measurement geometry, and constraints of the target. For example, dynamical systems are harder targets than static ones. The harder and noisier the setting becomes, the more emphasis goes on mathematical modeling of the targets. Bayesian statistical inversion is a common choice for difficult measurement settings, and its limitations mainly come from the choice of the a priori models. Gaussian models are widely studied, but they provide smooth reconstructions. Total variation priors are not invariant under mesh changes, so doing systematic uncertainty quantification, like data-centric sensor optimization, cannot be done with them. Besov and Cauchy priors however provide systematic non-Gaussian random field models, which can be used for contrast-boosting tomography. The drawback is higher computational cost. Hence, the techniques developed here are useful for non–time-critical applications with difficult measurement settings. In these cases, the methods developed may provide significantly better reconstructions than the traditional methods, like filtered back-projection.
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用以数据为中心的统计方法增强工业X射线断层扫描
摘要x射线层析成像技术应用于各种工业领域,如锯木厂、石油和天然气工业,以及化学、生物医学和岩土工程。本文研究了贝叶斯方法在x射线断层成像重建中的应用。在贝叶斯方法中,利用统计先验分布来解决层析重建的逆问题,该分布通过分配物体平滑度和边缘分布的概率来编码可能的内部结构。我们将高斯随机场先验(有利于平滑)与非高斯总变差(TV)、Besov和Cauchy先验(促进物体中的尖锐边缘和高对比度和低对比度区域)进行比较。我们还提出了求解100,000-1,000,000未知数的高维贝叶斯反问题的计算方案。我们研究了哈密顿蒙特卡罗(HMC)方法的无u -turn变体和更经典的自适应Metropolis-within-Gibbs (MwG)算法的适用性,以实现重建的完全不确定性量化。我们使用最大后验(MAP)估计有限内存BFGS (Broyden-Fletcher-Goldfarb-Shanno)优化算法。作为第一个工业应用,我们考虑了锯木厂的x射线测井层析成像。原木有结、腐烂的部分,甚至可能有金属碎片,这使它们成为非高斯先验的好例子。其次,以油气行业为例,对岩心层析成像进行了研究。在这种情况下,我们比较先验而不进行不确定性量化。我们表明,柯西先验比其他选择产生的伪象数量更少,特别是在稀疏的高噪声测量中,选择HMC可以实现系统的不确定性量化,前提是后验不是病态的多模态或重尾。工业x射线层析成像重建的精度取决于各种因素,如设备、测量几何形状和目标的约束。例如,动态系统是比静态系统更难对付的目标。设置的难度和噪声越大,目标的数学建模就越重要。贝叶斯统计反演是测量难度较大的一种常用方法,其局限性主要来自于对先验模型的选择。高斯模型得到了广泛的研究,但它们提供了平滑的重建。总变差先验在网格变化下不是不变的,因此无法进行系统的不确定性量化,如以数据为中心的传感器优化。然而,Besov和Cauchy先验提供了系统的非高斯随机场模型,可用于对比度增强层析成像。缺点是计算成本较高。因此,这里开发的技术对于具有困难测量设置的非时间关键应用非常有用。在这些情况下,所开发的方法可能比传统方法(如滤波反投影)提供更好的重建效果。
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来源期刊
DataCentric Engineering
DataCentric Engineering Engineering-General Engineering
CiteScore
5.60
自引率
0.00%
发文量
26
审稿时长
12 weeks
期刊最新文献
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