Bayesian Maximum Entropy Image Reconstruction

Abstract

This paper presents a Bayesian interpretation of maximum entropy image reconstruction and shows that exp(αS(/, m)), where S(f,m) is the entropy of image / relative to model m, is the only consistent prior probability distribution for positive, additive images. It also leads to a natural choice for the regularizing parameter α, that supersedes the traditional practice of setting χ = N. The new condition is that the dimensionless measure of structure — 2aS should be equal to the number of good singular values contained in the data. The performance of this new condition is discussed with reference to image deconvolution, but leads to a reconstruction that is visually disappointing. A deeper hypothesis space is proposed that overcomes these difficulties, by allowing for spatial correlations across the image.

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