Bayesian Abel inversion in quantitative Xray radiography
Abstract
A common image formation process in highenergy Xray radiography is to have a pulsed power source that emits Xrays through a scene, a scintillator that absorbs Xrays and fluoresces in the visible spectrum in response to the absorbed photons, and a chargecoupled device camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the inverse Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type and scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from Xray 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 density profile, the prior precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a jointmore »
 Authors:

 National Securities Technologies, LLC, Las Vegas, NV (United States)
 Holliston, MA (United States)
 Univ. of Alabama, Huntsville, AL (United States)
 Publication Date:
 Research Org.:
 Nevada Test Site/National Security Technologies, LLC, Las Vegas, NV (United States); Nevada Test Site (NTS), Mercury, NV (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Security (NA70); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA10)
 OSTI Identifier:
 1329259
 Alternate Identifier(s):
 OSTI ID: 1325541
 Report Number(s):
 DOE/NV/259462439
Journal ID: ISSN 10648275
 Grant/Contract Number:
 AC5206NA25946
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; Xray radiography; inverse problems; Bayesian inference; Markov Chain Monte Carlo; maximum likelihood estimation; Xray Radiography; Bayesian Inference
Citation Formats
Howard, Marylesa, Fowler, Michael, Luttman, Aaron, Mitchell, Stephen E., and Hock, Margaret C. Bayesian Abel inversion in quantitative Xray radiography. United States: N. p., 2016.
Web. doi:10.1137/15M1018721.
Howard, Marylesa, Fowler, Michael, Luttman, Aaron, Mitchell, Stephen E., & Hock, Margaret C. Bayesian Abel inversion in quantitative Xray radiography. United States. doi:10.1137/15M1018721.
Howard, Marylesa, Fowler, Michael, Luttman, Aaron, Mitchell, Stephen E., and Hock, Margaret C. Thu .
"Bayesian Abel inversion in quantitative Xray radiography". United States. doi:10.1137/15M1018721. https://www.osti.gov/servlets/purl/1329259.
@article{osti_1329259,
title = {Bayesian Abel inversion in quantitative Xray radiography},
author = {Howard, Marylesa and Fowler, Michael and Luttman, Aaron and Mitchell, Stephen E. and Hock, Margaret C.},
abstractNote = {A common image formation process in highenergy Xray radiography is to have a pulsed power source that emits Xrays through a scene, a scintillator that absorbs Xrays and fluoresces in the visible spectrum in response to the absorbed photons, and a chargecoupled device camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the inverse Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type and scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from Xray 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 density profile, the prior precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density profile, the prior parameters, and the spatial structure of the precision matrix. Lastly, results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy Xray imaging facility.},
doi = {10.1137/15M1018721},
journal = {SIAM Journal on Scientific Computing},
number = 3,
volume = 38,
place = {United States},
year = {2016},
month = {5}
}