Bayesian Comparison of Models for Images

A H Barnett and David J C MacKay

Probabilistic models for images are analysed quantitatively using Bayesian hypothesis comparison on a set of image data sets. One motivation for this study is to produce models which can be used as better {\em priors} in image reconstruction problems. The types of model vary from the simplest, where spatial correlations in the image are irrelevant, to more complicated ones based on a radial power law for the standard deviations of the coefficients produced by Fourier or Wavelet Transforms. In our experiments the Fourier model is the most successful, as its {\em evidence} is conclusively the highest. This ties in with the statistical scaling self-similarity (fractal property) of many images. We discuss the invariances of the models, and make suggestions for further investigations.

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