Applications of maximum entropy data analysis

McLean, Andrew Lister (1995) Applications of maximum entropy data analysis. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The work described here involved the application of the well established technique of maximum entropy data analysis to a number of experimental problems where it was not thought to have previously been used. Three real experimental problems were considered: the determination of magnetic hyperfine field distributions from overlapped Mössbauer spectra, the determination of particle size distributions from light scattering from particles of unknown shape and the merging of panchromatic and multispectral data in geographical remote sensing. In addition the more general theoretical problem of estimating distributions from samples is considered, which, though it is treated theoretically, was motivated by an enquiry from a spectroscopist.

The common factor shared by the three applications of maximum entropy to real problems is the presence of additional, so called, nuisance parameters which it was not feasible to marginalize out of the problem. The approach taken was to fix these parameters such that the entropy of the distribution we wish to determine was maximised. This procedure was applied successfully to all three cases. It should be noted that this procedure produces the 'most conservative' possible solution, as any other solution consistent with the data would have a lower entropy, and thus contain more information.

The individual problems also produced their own conclusions.

The light scattering problem demonstrated that there was information in the scattering pattern about the size distribution of particles, even when the data analysis allowed for the possibility that the particles were not of a uniform shape.

The investigation of the problem of merging panchromatic and multispectral images produced successful maximum entropy based reconstructions which were better than the conventional techniques with which they were compared. Though, this was achieved only at the cost of orders of magnitude more computing power. In addition, the physics based approach to the problem resulted in a better understanding of the current techniques. In particular a generalization of the intensity-hue-saturation technique, called generalized IHS, or GIHS, has been developed. (DX192,694)

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