, Volume 18, Issue 3, pp 165-174

Maximum entropy analysis of oversampled data problems

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Abstract

An algorithm for the solution of the Maximum Entropy problem is presented, for use when the data are considerably oversampled, so that the amount of independent information they contain is very much less than the actual number of data points. The application of general purpose entropy maximisation methods is then comparatively inefficient. In this algorithm the independent variables are in the singular space of the transform between map (or image or spectrum) and data. These variables are much fewer in number than either the data or the reconstructed map, resulting in a fast and accurate algorithm. The speed of this algorithm makes feasible the incorporation of recent ideas in maximum entropy theory (Skilling 1989 a; Gull 1989). This algorithm is particularly appropriate for the exponential decay problem, solution scattering, fibre diffraction, and similar applications.