von Mises-Fisher approximation of multiple scattering process on the hypersphere

International audienceThis paper presents a ''method of moments'' estimation technique for the study of multiple scattering on the hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particules in random media

VON MISES-FISHER APPROXIMATION OF MULTIPLE SCATTERING PROCESS ON THE HYPERSPHERE

This paper presents a “method of moments ” estimation technique for the study of multiple scattering on the hypersphere. The proposed model is similar to a compound Poisson process evolving on a special manifold: the unit hypersphere. The presented work makes use of an approximation result for multiply convolved von Mises-Fisher distributions on hyperspheres. Comparison with other approximations show the accuracy of the proposed model to provide estimators for the mean free path and concentration parameters when studying a multiple scattering process. Such a process is classically used to model the propagation of waves or particules in random media. Index Terms — von Mises-Fisher distribution, random walk on hypersphere, multiple scattering, Method of moments estimation. 1