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Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

Author

Listed:
  • Thon, Kevin
  • Rue, Håvard
  • Skrøvseth, Stein Olav
  • Godtliebsen, Fred

Abstract

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.

Suggested Citation

  • Thon, Kevin & Rue, Håvard & Skrøvseth, Stein Olav & Godtliebsen, Fred, 2012. "Bayesian multiscale analysis of images modeled as Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 49-61, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:49-61
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    References listed on IDEAS

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    1. Ian L. Dryden & Mark R. Scarr & Charles C. Taylor, 2003. "Bayesian texture segmentation of weed and crop images using reversible jump Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 31-50, January.
    2. Godtliebsen, Fred & Oigard, Tor Arne, 2005. "A visual display device for significant features in complicated signals," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 317-343, February.
    3. Oigard, Tor Arne & Rue, Havard & Godtliebsen, Fred, 2006. "Bayesian multiscale analysis for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1719-1730, December.
    4. Holmström, Lasse & Pasanen, Leena & Furrer, Reinhard & Sain, Stephan R., 2011. "Scale space multiresolution analysis of random signals," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2840-2855, October.
    5. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
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    Cited by:

    1. Maria‐Zafeiria Spyropoulou & James Bentham, 2024. "Scaling priors for intrinsic Gaussian Markov random fields applied to blood pressure data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 491-504, August.
    2. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.
    3. Hotz, Thomas & Marnitz, Philipp & Stichtenoth, Rahel & Davies, Laurie & Kabluchko, Zakhar & Munk, Axel, 2012. "Locally adaptive image denoising by a statistical multiresolution criterion," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 543-558.

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