skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Spatial Signal Detection Using Continuous Shrinkage Priors

Abstract

Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. As a result, we apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.

Authors:
 [1];  [2];  [1];  [1]; ORCiD logo [3];  [1];  [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Virginia Commonwealth Univ., Richmond, VA (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1504020
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Technometrics
Additional Journal Information:
Journal Volume: 61; Journal Issue: 4; Journal ID: ISSN 0040-1706
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Bayesian variable selection; High-dimensional data; Image analysis; X-ray diffraction

Citation Formats

Jhuang, An -Ting, Fuentes, Montserrat, Jones, Jacob L., Esteves, Giovanni, Fancher, Chris M., Furman, Marschall, and Reich, Brian J. Spatial Signal Detection Using Continuous Shrinkage Priors. United States: N. p., 2019. Web. doi:10.1080/00401706.2018.1546622.
Jhuang, An -Ting, Fuentes, Montserrat, Jones, Jacob L., Esteves, Giovanni, Fancher, Chris M., Furman, Marschall, & Reich, Brian J. Spatial Signal Detection Using Continuous Shrinkage Priors. United States. doi:10.1080/00401706.2018.1546622.
Jhuang, An -Ting, Fuentes, Montserrat, Jones, Jacob L., Esteves, Giovanni, Fancher, Chris M., Furman, Marschall, and Reich, Brian J. Fri . "Spatial Signal Detection Using Continuous Shrinkage Priors". United States. doi:10.1080/00401706.2018.1546622. https://www.osti.gov/servlets/purl/1504020.
@article{osti_1504020,
title = {Spatial Signal Detection Using Continuous Shrinkage Priors},
author = {Jhuang, An -Ting and Fuentes, Montserrat and Jones, Jacob L. and Esteves, Giovanni and Fancher, Chris M. and Furman, Marschall and Reich, Brian J.},
abstractNote = {Motivated by the problem of detecting changes in two-dimensional X-ray diffraction data, we propose a Bayesian spatial model for sparse signal detection in image data. Our model places considerable mass near zero and has heavy tails to reflect the prior belief that the image signal is zero for most pixels and large for an important subset. We show that the spatial prior places mass on nearby locations simultaneously being zero, and also allows for nearby locations to simultaneously be large signals. The form of the prior also facilitates efficient computing for large images. We conduct a simulation study to evaluate the properties of the proposed prior and show that it outperforms other spatial models. As a result, we apply our method in the analysis of X-ray diffraction data from a two-dimensional area detector to detect changes in the pattern when the material is exposed to an electric field.},
doi = {10.1080/00401706.2018.1546622},
journal = {Technometrics},
number = 4,
volume = 61,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Inference with normal-gamma prior distributions in regression problems
journal, March 2010

  • Griffin, Jim E.; Brown, Philip J.
  • Bayesian Analysis, Vol. 5, Issue 1
  • DOI: 10.1214/10-BA507

The what, how, and why of wavelet shrinkage denoising
journal, January 2000


Variable Selection via Gibbs Sampling
journal, September 1993


The horseshoe estimator: Posterior concentration around nearly black vectors
journal, January 2014

  • van der Pas, S. L.; Kleijn, B. J. K.; van der Vaart, A. W.
  • Electronic Journal of Statistics, Vol. 8, Issue 2
  • DOI: 10.1214/14-EJS962

Bayesian Variable Selection in Linear Regression
journal, December 1988


Anomaly Detection in Images With Smooth Background via Smooth-Sparse Decomposition
journal, January 2017


In situ characterization of polycrystalline ferroelectrics using x-ray and neutron diffraction
journal, November 2014

  • Esteves, Giovanni; Fancher, Chris M.; Jones, Jacob L.
  • Journal of Materials Research, Vol. 30, Issue 3
  • DOI: 10.1557/jmr.2014.302

Ideal spatial adaptation by wavelet shrinkage
journal, September 1994


Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review
journal, September 2017


The Estimation of Prediction Error: Covariance Penalties and Cross-Validation
journal, September 2004


Efficient Empirical Bayes Variable Selection and Estimation in Linear Models
journal, December 2005


Application of the Radon transform to detect small-targets in sea clutter
journal, January 2009

  • Carretero-Moya, J.; Gismero-Menoyo, J.; Asensio-López, A.
  • IET Radar, Sonar & Navigation, Vol. 3, Issue 2
  • DOI: 10.1049/iet-rsn:20080123

Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank
journal, April 2011

  • Xu, Jia; Yu, Ji; Peng, Ying-Ning
  • IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, Issue 2
  • DOI: 10.1109/TAES.2011.5751251

Bayesian Model Selection in High-Dimensional Settings
journal, June 2012


The horseshoe estimator for sparse signals
journal, April 2010


Asymptotic Properties of Bayes Risk for the Horseshoe Prior
journal, March 2013

  • Datta, Jyotishka; Ghosh, Jayanta. K.
  • Bayesian Analysis, Vol. 8, Issue 1
  • DOI: 10.1214/13-BA805

Convolutional neural networks: an overview and application in radiology
journal, June 2018

  • Yamashita, Rikiya; Nishio, Mizuho; Do, Richard Kinh Gian
  • Insights into Imaging, Vol. 9, Issue 4
  • DOI: 10.1007/s13244-018-0639-9

The Spike-and-Slab LASSO
text, January 2019


High-pressure crystallography
journal, December 2007

  • Katrusiak, Andrzej
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 64, Issue 1
  • DOI: 10.1107/S0108767307061181

Default Bayesian analysis with global-local shrinkage priors
journal, December 2016

  • Bhadra, Anindya; Datta, Jyotishka; Polson, Nicholas G.
  • Biometrika, Vol. 103, Issue 4
  • DOI: 10.1093/biomet/asw041

A review of Bayesian variable selection methods: what, how and which
journal, March 2009

  • O'Hara, R. B.; Sillanpää, M. J.
  • Bayesian Analysis, Vol. 4, Issue 1
  • DOI: 10.1214/09-BA403

Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection
journal, January 2014

  • Goldsmith, Jeff; Huang, Lei; Crainiceanu, Ciprian M.
  • Journal of Computational and Graphical Statistics, Vol. 23, Issue 1
  • DOI: 10.1080/10618600.2012.743437

False discovery control in large-scale spatial multiple testing
journal, April 2014

  • Sun, Wenguang; Reich, Brian J.; Tony Cai, T.
  • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 77, Issue 1
  • DOI: 10.1111/rssb.12064

Sparse inverse covariance estimation with the graphical lasso
journal, December 2007


Bayesian Variable Selection in Linear Regression
journal, December 1988

  • Mitchell, T. J.; Beauchamp, J. J.
  • Journal of the American Statistical Association, Vol. 83, Issue 404
  • DOI: 10.2307/2290129

The Spike-and-Slab LASSO
journal, September 2017


The birth of X-ray crystallography
journal, November 2012


Ideal Spatial Adaptation by Wavelet Shrinkage
journal, August 1994

  • Donoho, David L.; Johnstone, Iain M.
  • Biometrika, Vol. 81, Issue 3
  • DOI: 10.2307/2337118

A spatial scan statistic
journal, January 1997


Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition
journal, June 2017


An Improved Acceptance Procedure for the Hybrid Monte Carlo Algorithm
journal, March 1994


On the determination of functions from their integral values along certain manifolds
journal, December 1986


Pathwise coordinate optimization
journal, December 2007

  • Friedman, Jerome; Hastie, Trevor; Höfling, Holger
  • The Annals of Applied Statistics, Vol. 1, Issue 2
  • DOI: 10.1214/07-AOAS131

High-resolution x-ray diffraction study of single crystals of lead zirconate titanate
journal, July 2011


Adaptive Thresholding using the Integral Image
journal, January 2007


Spatial Modeling With Spatially Varying Coefficient Processes
journal, June 2003

  • Gelfand, Alan E.; Kim, Hyon-Jung; Sirmans, C. F.
  • Journal of the American Statistical Association, Vol. 98, Issue 462
  • DOI: 10.1198/016214503000170

Scalar-on-image regression via the soft-thresholded Gaussian process
journal, January 2018

  • Kang, Jian; Reich, Brian J.; Staicu, Ana-Maria
  • Biometrika, Vol. 105, Issue 1
  • DOI: 10.1093/biomet/asx075

The Distribution of the Size of the Maximum Cluster of Points on a Line
journal, June 1965


The Spike-and-Slab LASSO
text, January 2019


Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression
journal, June 2015

  • Li, Fan; Zhang, Tingting; Wang, Quanli
  • The Annals of Applied Statistics, Vol. 9, Issue 2
  • DOI: 10.1214/15-AOAS818

Jump Detection in Regression Surfaces
journal, September 1997

  • Qiu, Peihua; Yandell, Brian
  • Journal of Computational and Graphical Statistics, Vol. 6, Issue 3
  • DOI: 10.2307/1390737

BaySTDetect: detecting unusual temporal patterns in small area data via Bayesian model choice
journal, March 2012


An integrated index for identification of fatty liver disease using radon transform and discrete cosine transform features in ultrasound images
journal, September 2016


Radon-Domain Detection of the Nipple and the Pectoral Muscle in Mammograms
journal, April 2007

  • Kinoshita, S. K.; Azevedo-Marques, P. M.; Pereira, R. R.
  • Journal of Digital Imaging, Vol. 21, Issue 1
  • DOI: 10.1007/s10278-007-9035-6

Bayesian Methods for High Dimensional Linear Models
journal, January 2013


Automatic assessment of macular edema from color retinal images
journal, March 2012


Uncertainty Quantification for the Horseshoe (with Discussion)
journal, December 2017

  • van der Pas, Stéphanie; Szabó, Botond; van der Vaart, Aad
  • Bayesian Analysis, Vol. 12, Issue 4
  • DOI: 10.1214/17-BA1065

Blur kernel estimation using the radon transform
conference, June 2011

  • Cho, Taeg Sang; Paris, Sylvain; Horn, Berthold K. P.
  • 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), CVPR 2011
  • DOI: 10.1109/CVPR.2011.5995479

    Works referencing / citing this record:

    An Improved Acceptance Procedure for the Hybrid Monte Carlo Algorithm
    journal, March 1994


    Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank
    journal, April 2011

    • Xu, Jia; Yu, Ji; Peng, Ying-Ning
    • IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, Issue 2
    • DOI: 10.1109/taes.2011.5751251

    A review of Bayesian variable selection methods: what, how and which
    journal, March 2009

    • O'Hara, R. B.; Sillanpää, M. J.
    • Bayesian Analysis, Vol. 4, Issue 1
    • DOI: 10.1214/09-ba403

    A spatial scan statistic
    journal, January 1997


    The Spike-and-Slab LASSO
    journal, September 2017


    Pathwise coordinate optimization
    journal, December 2007

    • Friedman, Jerome; Hastie, Trevor; Höfling, Holger
    • The Annals of Applied Statistics, Vol. 1, Issue 2
    • DOI: 10.1214/07-aoas131

    Jump Detection in Regression Surfaces
    journal, September 1997

    • Qiu, Peihua; Yandell, Brian
    • Journal of Computational and Graphical Statistics, Vol. 6, Issue 3
    • DOI: 10.2307/1390737

    An integrated index for identification of fatty liver disease using radon transform and discrete cosine transform features in ultrasound images
    journal, September 2016


    Spatial Modeling With Spatially Varying Coefficient Processes
    journal, June 2003

    • Gelfand, Alan E.; Kim, Hyon-Jung; Sirmans, C. F.
    • Journal of the American Statistical Association, Vol. 98, Issue 462
    • DOI: 10.1198/016214503000170

    The horseshoe estimator for sparse signals
    journal, April 2010


    Adaptive Thresholding using the Integral Image
    journal, January 2007


    False discovery control in large-scale spatial multiple testing
    journal, April 2014

    • Sun, Wenguang; Reich, Brian J.; Tony Cai, T.
    • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 77, Issue 1
    • DOI: 10.1111/rssb.12064

    Real-Time Monitoring of High-Dimensional Functional Data Streams via Spatio-Temporal Smooth Sparse Decomposition
    journal, June 2017


    Ideal spatial adaptation by wavelet shrinkage
    journal, September 1994


    The Estimation of Prediction Error: Covariance Penalties and Cross-Validation
    journal, September 2004


    Anomaly Detection in Images With Smooth Background via Smooth-Sparse Decomposition
    journal, January 2017


    Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection
    journal, January 2014

    • Goldsmith, Jeff; Huang, Lei; Crainiceanu, Ciprian M.
    • Journal of Computational and Graphical Statistics, Vol. 23, Issue 1
    • DOI: 10.1080/10618600.2012.743437

    The Distribution of the Size of the Maximum Cluster of Points on a Line
    journal, June 1965


    BaySTDetect: detecting unusual temporal patterns in small area data via Bayesian model choice
    journal, March 2012


    Automatic assessment of macular edema from color retinal images
    journal, March 2012


    Radon-Domain Detection of the Nipple and the Pectoral Muscle in Mammograms
    journal, April 2007

    • Kinoshita, S. K.; Azevedo-Marques, P. M.; Pereira, R. R.
    • Journal of Digital Imaging, Vol. 21, Issue 1
    • DOI: 10.1007/s10278-007-9035-6

    Scalar-on-image regression via the soft-thresholded Gaussian process
    journal, January 2018

    • Kang, Jian; Reich, Brian J.; Staicu, Ana-Maria
    • Biometrika, Vol. 105, Issue 1
    • DOI: 10.1093/biomet/asx075

    Efficient Empirical Bayes Variable Selection and Estimation in Linear Models
    journal, December 2005


    Application of the Radon transform to detect small-targets in sea clutter
    journal, January 2009

    • Carretero-Moya, J.; Gismero-Menoyo, J.; Asensio-López, A.
    • IET Radar, Sonar & Navigation, Vol. 3, Issue 2
    • DOI: 10.1049/iet-rsn:20080123

    The horseshoe estimator: Posterior concentration around nearly black vectors
    journal, January 2014

    • van der Pas, S. L.; Kleijn, B. J. K.; van der Vaart, A. W.
    • Electronic Journal of Statistics, Vol. 8, Issue 2
    • DOI: 10.1214/14-ejs962

    Bayesian Methods for High Dimensional Linear Models
    journal, January 2013


    Inference with normal-gamma prior distributions in regression problems
    journal, March 2010

    • Griffin, Jim E.; Brown, Philip J.
    • Bayesian Analysis, Vol. 5, Issue 1
    • DOI: 10.1214/10-ba507

    Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression
    journal, June 2015

    • Li, Fan; Zhang, Tingting; Wang, Quanli
    • The Annals of Applied Statistics, Vol. 9, Issue 2
    • DOI: 10.1214/15-aoas818

    Convolutional neural networks: an overview and application in radiology
    journal, June 2018

    • Yamashita, Rikiya; Nishio, Mizuho; Do, Richard Kinh Gian
    • Insights into Imaging, Vol. 9, Issue 4
    • DOI: 10.1007/s13244-018-0639-9

    Bayesian Variable Selection in Linear Regression
    journal, December 1988


    High-pressure crystallography
    journal, December 2007

    • Katrusiak, Andrzej
    • Acta Crystallographica Section A Foundations of Crystallography, Vol. 64, Issue 1
    • DOI: 10.1107/s0108767307061181

    Default Bayesian analysis with global-local shrinkage priors
    journal, December 2016

    • Bhadra, Anindya; Datta, Jyotishka; Polson, Nicholas G.
    • Biometrika, Vol. 103, Issue 4
    • DOI: 10.1093/biomet/asw041

    Bayesian Model Selection in High-Dimensional Settings
    journal, June 2012


    The birth of X-ray crystallography
    journal, November 2012


    Sparse inverse covariance estimation with the graphical lasso
    journal, December 2007


    Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review
    journal, September 2017


    Asymptotic Properties of Bayes Risk for the Horseshoe Prior
    journal, March 2013

    • Datta, Jyotishka; Ghosh, Jayanta. K.
    • Bayesian Analysis, Vol. 8, Issue 1
    • DOI: 10.1214/13-ba805

    On the determination of functions from their integral values along certain manifolds
    journal, December 1986


    High-resolution x-ray diffraction study of single crystals of lead zirconate titanate
    journal, July 2011


    In situ characterization of polycrystalline ferroelectrics using x-ray and neutron diffraction
    journal, November 2014

    • Esteves, Giovanni; Fancher, Chris M.; Jones, Jacob L.
    • Journal of Materials Research, Vol. 30, Issue 3
    • DOI: 10.1557/jmr.2014.302

    Variable Selection via Gibbs Sampling
    journal, September 1993


    Uncertainty Quantification for the Horseshoe (with Discussion)
    journal, December 2017

    • van der Pas, Stéphanie; Szabó, Botond; van der Vaart, Aad
    • Bayesian Analysis, Vol. 12, Issue 4
    • DOI: 10.1214/17-ba1065

    The what, how, and why of wavelet shrinkage denoising
    journal, January 2000