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Title: Bayesian Abel Inversion in Quantitative X-Ray Radiography

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and uoresces in the visible spectrum in response to the absorbed photons, and a CCD 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 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 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 density pro le, the data precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posteriormore » distribution for the unknown density pro le, the prior parameters, and the spatial structure of the precision matrix. 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 X-ray imaging facility.« less
 [1] ;  [1] ;  [1] ;  [1] ;  [2]
  1. National Security Technologies, LLC. (NSTec), Mercury, NV (United States)
  2. Univ. of Alabama, Huntsville, AL (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1064-8275
Grant/Contract Number:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 1064-8275
Research Org:
Nevada Test Site (NTS), Mercury, NV (United States); Nevada Test Site/National Security Technologies, LLC, Las Vegas, NV (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10); USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Security (NA-70)
Country of Publication:
United States
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; X-ray Radiography; Inverse Problems; Bayesian Inference; Markov Chain Monte Carlo; Maximum Likelihood Estimation; X-ray radiography; inverse problems; Bayesian inference; maximum likelihood estimation
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1325541