Generalized Uncertainty Quantification for Linear Inverse Problems in Xray Imaging
Abstract
In industrial and engineering applications, Xray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy Xrays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in Xray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and developmore »
 Authors:

 Clarkson Univ., Potsdam, NY (United States)
 Publication Date:
 Research Org.:
 Nevada Test Site/National Security Technologies, LLC, Las Vegas, NV (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1179471
 Report Number(s):
 DOE/NV/259462051
 DOE Contract Number:
 AC5206NA25946
 Resource Type:
 Thesis/Dissertation
 Country of Publication:
 United States
 Language:
 English
 Subject:
 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY
Citation Formats
Fowler, Michael James. Generalized Uncertainty Quantification for Linear Inverse Problems in Xray Imaging. United States: N. p., 2014.
Web. doi:10.2172/1179471.
Fowler, Michael James. Generalized Uncertainty Quantification for Linear Inverse Problems in Xray Imaging. United States. https://doi.org/10.2172/1179471
Fowler, Michael James. 2014.
"Generalized Uncertainty Quantification for Linear Inverse Problems in Xray Imaging". United States. https://doi.org/10.2172/1179471. https://www.osti.gov/servlets/purl/1179471.
@article{osti_1179471,
title = {Generalized Uncertainty Quantification for Linear Inverse Problems in Xray Imaging},
author = {Fowler, Michael James},
abstractNote = {In industrial and engineering applications, Xray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy Xrays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in Xray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edgelocalizing prior for deconvolution; a smoothing prior with nonnegativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy laboratories.},
doi = {10.2172/1179471},
url = {https://www.osti.gov/biblio/1179471},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2014},
month = {4}
}