A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

Fowler, Michael J.; Howard, Marylesa; Luttman, Aaron; Mitchell, Stephen E.; Webb, Timothy J.

doi:10.1080/17415977.2015.1046859

Title: A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

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Abstract

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Lastly, synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.

Authors:

Fowler, Michael J. ^[1]; Howard, Marylesa ^[1]; Luttman, Aaron ^[1]; Mitchell, Stephen E. ^[1]; Webb, Timothy J. ^[2]

National Security Technologies, LLC, North Las Vegas, NV (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Wed Jun 03 00:00:00 EDT 2015

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1142174

Report Number(s):: SAND-2014-2872J
Journal ID: ISSN 1741-5977; 507350

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Inverse Problems in Science and Engineering

Additional Journal Information:: Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 1741-5977

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; inverse problems; pulsed power; X-ray radiography; Markov chain Monte Carlo; uncertainty quantification; bound constrained optimization

Citation Formats


                    Fowler, Michael J., Howard, Marylesa, Luttman, Aaron, Mitchell, Stephen E., and Webb, Timothy J. A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems.  United States: N. p., 2015. 
Web.  doi:10.1080/17415977.2015.1046859.

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                    Fowler, Michael J., Howard, Marylesa, Luttman, Aaron, Mitchell, Stephen E., & Webb, Timothy J. A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems.  United States.  https://doi.org/10.1080/17415977.2015.1046859

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                    Fowler, Michael J., Howard, Marylesa, Luttman, Aaron, Mitchell, Stephen E., and Webb, Timothy J. Wed .  
"A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems".  United States.  https://doi.org/10.1080/17415977.2015.1046859.  https://www.osti.gov/servlets/purl/1142174.

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@article{osti_1142174,

  title        = {A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems},

  author       = {Fowler, Michael J. and Howard, Marylesa and Luttman, Aaron and Mitchell, Stephen E. and Webb, Timothy J.},

  abstractNote = {One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Lastly, synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.},

  doi          = {10.1080/17415977.2015.1046859},

  journal      = {Inverse Problems in Science and Engineering},

  number       = 3,

  volume       = 24,

  place        = {United States},

  year         = {Wed Jun 03 00:00:00 EDT 2015},

  month        = {Wed Jun 03 00:00:00 EDT 2015}

}

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