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Bayesian image restoration, with two applications in spatial statistics

Annals of the Institute of Statistical Mathematics volume 43, pages 1–20 (1991)Cite this article

Abstract

There has been much recent interest in Bayesian image analysis, including such topics as removal of blur and noise, detection of object boundaries, classification of textures, and reconstruction of two- or three-dimensional scenes from noisy lower-dimensional views. Perhaps the most straightforward task is that of image restoration, though it is often suggested that this is an area of relatively minor practical importance. The present paper argues the contrary, since many problems in the analysis of spatial data can be interpreted as problems of image restoration. Furthermore, the amounts of data involved allow routine use of computer intensive methods, such as the Gibbs sampler, that are not yet practicable for conventional images. Two examples are given, one in archeology, the other in epidemiology. These are preceded by a partial review of pixel-based Bayesian image analysis.

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Author notes

  1. Julian Besag

    Present address: Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, Newcastle upon Tyne, U.K.

Authors and Affiliations

  1. Department of Statistics GN-22, University of Washington, 98195, Seattle, WA, U.S.A.

    Julian Besag & Jeremy York

  2. Institut Gustave Roussy, INSERM U287, 94805, Villejuif Cedex, France

    Annie Mollié

Authors
  1. Julian Besag
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  2. Jeremy York
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  3. Annie Mollié
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Additional information

An earlier version of this article was presented at the symposium on the Analysis of Statistical Information held in the Institute of Statistical Mathematics, Tokyo during December 5–8, 1989.

This research was carried out partly at the University of Durham, U.K., with the support of an award by the Complex Stochastic Systems Initiative of the Science and Engineering Research Council.

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Besag, J., York, J. & Mollié, A. Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 43, 1–20 (1991). https://doi.org/10.1007/BF00116466

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  • DOI: https://doi.org/10.1007/BF00116466

Key words and phrases

  • Bayesian restoration
  • image analysis
  • spatial statistics
  • Gibbs sampler
  • archeology
  • epidemiology