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Volume 27, Issue 5
Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography

Xinge Li, Haibo Xu, Na Zheng, Qinggang Jia, Tongxiang Gu & Suhua Wei

DOI: 10.4208/cicp.OA-2019-0060

Commun. Comput. Phys., 27 (2020), pp. 1485-1504.

Published online: 2020-03

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  • Abstract

High-energy X-ray radiography is a measuring technique for quantitative measurement and diagnosis of the object and its internal structure. Tomographic reconstruction determines the geometric and physical properties of the object according to the energy distribution on the imaging plane. Considering the noise and blur in the process of radiographing, we construct a general reconstruction model for the axisymmetric single image photographic system. This inverse problem is then cast within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown nonnegative density profile, the precision matrix, and two scale parameters. This results in a joint posterior distribution, which can be readily sampled using the Markov chain Monte Carlo (MCMC) method. To study the role of hyperparameters and their sensitivity analysis, a wide variety of tests were conducted which led to a number of definitive conclusions. Results of the density reconstructions and pointwise uncertainty estimates are presented for simulated signals with various physical factors in the imaging process included.

  • Keywords

Inverse problem, density reconstruction, uncertainty quantification, Bayesian inference, MCMC method.

  • AMS Subject Headings

65K99, 65Z05, 62F15, 62P35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lixinge@lsec.cc.ac.cn (Xinge Li)

xu haibo@iapcm.ac.cn (Haibo Xu)

zheng na@iapcm.ac.cn (Na Zheng)

QGJIA XJTU@126.com (Qinggang Jia)

txgu@iapcm.ac.cn (Tongxiang Gu)

wei suhua@iapcm.ac.cn (Suhua Wei)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1485, author = {Li , XingeXu , HaiboZheng , NaJia , QinggangGu , Tongxiang and Wei , Suhua}, title = {Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {5}, pages = {1485--1504}, abstract = {

High-energy X-ray radiography is a measuring technique for quantitative measurement and diagnosis of the object and its internal structure. Tomographic reconstruction determines the geometric and physical properties of the object according to the energy distribution on the imaging plane. Considering the noise and blur in the process of radiographing, we construct a general reconstruction model for the axisymmetric single image photographic system. This inverse problem is then cast within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown nonnegative density profile, the precision matrix, and two scale parameters. This results in a joint posterior distribution, which can be readily sampled using the Markov chain Monte Carlo (MCMC) method. To study the role of hyperparameters and their sensitivity analysis, a wide variety of tests were conducted which led to a number of definitive conclusions. Results of the density reconstructions and pointwise uncertainty estimates are presented for simulated signals with various physical factors in the imaging process included.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0060}, url = {http://global-sci.org/intro/article_detail/cicp/15766.html} }
TY - JOUR T1 - Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography AU - Li , Xinge AU - Xu , Haibo AU - Zheng , Na AU - Jia , Qinggang AU - Gu , Tongxiang AU - Wei , Suhua JO - Communications in Computational Physics VL - 5 SP - 1485 EP - 1504 PY - 2020 DA - 2020/03 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2019-0060 UR - https://global-sci.org/intro/article_detail/cicp/15766.html KW - Inverse problem, density reconstruction, uncertainty quantification, Bayesian inference, MCMC method. AB -

High-energy X-ray radiography is a measuring technique for quantitative measurement and diagnosis of the object and its internal structure. Tomographic reconstruction determines the geometric and physical properties of the object according to the energy distribution on the imaging plane. Considering the noise and blur in the process of radiographing, we construct a general reconstruction model for the axisymmetric single image photographic system. This inverse problem is then cast within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown nonnegative density profile, the precision matrix, and two scale parameters. This results in a joint posterior distribution, which can be readily sampled using the Markov chain Monte Carlo (MCMC) method. To study the role of hyperparameters and their sensitivity analysis, a wide variety of tests were conducted which led to a number of definitive conclusions. Results of the density reconstructions and pointwise uncertainty estimates are presented for simulated signals with various physical factors in the imaging process included.

Li , XingeXu , HaiboZheng , NaJia , QinggangGu , Tongxiang and Wei , Suhua. (2020). Uncertainty Quantification of Density Reconstruction Using MCMC Method in High-Energy X-ray Radiography. Communications in Computational Physics. 27 (5). 1485-1504. doi:10.4208/cicp.OA-2019-0060
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