Bayesian Abel inversion in quantitative X-ray radiography
- National Securities Technologies, LLC, Las Vegas, NV (United States)
- Holliston, MA (United States)
- Univ. of Alabama, Huntsville, AL (United States)
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 posterior 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.
- Research Organization:
- Nevada Test Site/National Security Technologies, LLC, Las Vegas, NV (United States); Nevada Test Site (NTS), Mercury, NV (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Security; USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
- Grant/Contract Number:
- AC52-06NA25946
- OSTI ID:
- 1329259
- Alternate ID(s):
- OSTI ID: 1325541
- Report Number(s):
- DOE/NV/25946-2439
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 38, Issue 3; ISSN 1064-8275
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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