Developments in Maximum Entropy Data Analysis

The derivation of “Classic” MaxEnt is completed, showing that it leads to a natural choice for the regularising parameter α, that supersedes the traditional practice of setting x2=N, and the new condition is that the dimensionless measure of structure -2αS should be equal to the number of good singular values contained in the data.

Abstract

The Bayesian derivation of "Classic" MaxEnt image processing (Skilling 1989a) shows that exp(αS(f,m)), where S(f,m) is the entropy of image f relative to model m, is the only consistent prior probability distribution for positive, additive images. In this paper the derivation of "Classic" MaxEnt is completed, showing that it leads to a natural choice for the regularising parameter α, that supersedes the traditional practice of setting x2=N. The new condition is that the dimensionless measure of structure -2αS 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.