Moments and Classification for Conjugation-Invariant Rotations and Fake Uniformity in the Stochastic Radon Transform

Mathematics – Probability

Scientific paper

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14 pages, 1 figure

Scientific paper

We consider a generalisation of the stochastic Radon transform, introduced for an inverse problem in tomography by Panaretos. Specifically, we allow the distribution of the three-dimensional rotation in the statistical model of that work to be different from Haar measure, and to possess only the weaker symmetry property of conjugation-invariance. As a preparation we study, based on simple geometric ideas, the relationship between moments of two univariate densities describing conjugation-invariant rotations. For the class of rotations introduced by Le{\'o}n, Mass{\'e} and Rivest,the generalised stochastic Radon transform turns out to have a 'fake uniformity' property. We also derive the binary Bayes classifier for rotations whose distributions are deterministic shifts of a common conjugation-invariant distribution.

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