BAYESIAN IMAGE RESTORATION,

WITH TWO APPLICATIONS IN SPATIAL STATISTICS

JULIAN BESAG^{1}, JEREMY YORK^{1} AND ANNIE MOLLIÉ^{2}

1Department of Statistics GN-22, University of Washington, Seattle, WA 98195, U.S.A. 2Institut Gustave Roussy, INSERM U287, 94805 Villejuif Cedex, France

(Received November 7, 1989; revised June 18, 1990)

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.

Key words and phrases: Bayesian restoration, image analysis, spatial statistics, Gibbs sampler, archeology, epidemiology.