Bayesian image restoration, with two applications in spatial statistics
 Julian Besag,
 Jeremy York,
 Annie Mollié
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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 threedimensional scenes from noisy lowerdimensional 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 pixelbased Bayesian image analysis.
 Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems (with Discussion). J. Roy. Statist. Soc. Ser. B 36: pp. 192236
 Besag, J. E. (1975) Statistical analysis of nonlattice data. The Statistician 24: pp. 179195
 Besag, J. E. (1983) Discussion of paper by P. Switzer. Bull. Internat. Statist. Inst. 50: pp. 422425
 Besag, J. E. (1986) On the statistical analysis of dirty pictures (with Discussion). J. Roy. Statist. Soc. Ser. B 48: pp. 259302
 Besag, J. E. (1989) Towards Bayesian image analysis. Journal of Applied Statistics 16: pp. 395407
 Besag, J. E., Mollié, A. (1989) Bayesian mapping of mortality rates. Bull. Internat. Statist. Inst. 53: pp. 127128
 Breslow, N. E. (1984) ExtraPoisson variation in loglinear models. J. Roy. Statist. Soc. Ser. C 33: pp. 3844
 Buck, C. E., Cavanagh, W. G., Litton, C. D. (1988) The spatial analysis of soil phosphate data. Tech. Report. Department of Mathematics, University of Nottingham, U.K.
 Chow, Y., Grenander, U., Keenan, D. M. (1988) Hands: a pattern theoretic study of biological shape. Tech. Report. Division of Applied Mathematics, Brown University, Providence, Rhode Island
 Clayton, D., Kaldor, J. (1987) Empirical Bayes estimates of agestandardized relative risks for use in disease mapping. Biometrics 43: pp. 671681
 Geman, D., Geman, S. Bayesian image analysis. In: Bienenstock, E. eds. (1986) Disorderd Systems and Biological Organization. Springer, Berlin
 Geman, D., Geman, S., Graffigne, C., Ping, Dong (1990) Boundary detection by constrained optimization. I.E.E.E. Transactions: Pattern Analysis and Machine Intelligence 12: pp. 609628
 Geman, S., Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. I.E.E.E. Transactions: Pattern Analysis and Machine Intelligence 6: pp. 721741
 Geman, S. and Graffigne, C. (1987). Markov random field image models and their applications to computer vision, Proc. International Congress of Mathematicians (1986) (ed. A. M. Gleason), 1496–1517, Berkeley, California.
 Geman, S., McClure, D. (1987) Statistical methods for tomographic image reconstruction. Bull. Internat. Statist. Inst. 52: pp. 521
 Green, P. J. (1990) Penalized likelihood reconstructions from emission tomography data using a modified EM algorithm. I.E.E.E. Transactions: Medical Imaging 9: pp. 8493
 Greig, D. M., Porteous, B. T., Seheult, A. H. (1989) Exact maximum a posteriori estimation for binary images. J. Roy. Statist. Soc. Ser. B 51: pp. 271279
 Grenander, U. (1983) Tutorial in pattern theory. Tech. Report. Division of Applied Mathematics, Brown University, Providence, Rhode Island
 Kent, J. T., Mardia, K. V. (1988) Spatial classification using fuzzy membership models. I.E.E.E. Transactions: Pattern Analysis and Machine Intelligence 10: pp. 659671
 Künsch, H. R. (1987) Intrinsic autoregressions and related models on the twodimensional lattice. Biometrika 74: pp. 517524
 Mollié, A. (1990). Représentation géographique des taux de mortalité: modélisation spatiale et méthodes Bayésiennes (unpublished Ph. D. thesis).
 Owen, A. (1989) Image segmentation via iterated conditional expectations. Tech. Report. Department of Statistics, Stanford University, California
 Title
 Bayesian image restoration, with two applications in spatial statistics
 Journal

Annals of the Institute of Statistical Mathematics
Volume 43, Issue 1 , pp 120
 Cover Date
 19910301
 DOI
 10.1007/BF00116466
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Bayesian restoration
 image analysis
 spatial statistics
 Gibbs sampler
 archeology
 epidemiology
 Industry Sectors
 Authors

 Julian Besag ^{(1)}
 Jeremy York ^{(1)}
 Annie Mollié ^{(3)}
 Author Affiliations

 1. Department of Statistics GN22, University of Washington, 98195, Seattle, WA, U.S.A.
 3. Institut Gustave Roussy, INSERM U287, 94805, Villejuif Cedex, France