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 - <p style="text-align: justify;">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.</p>