Isotropic Multiple Scattering Processes on Hyperspheres

Nicolas Le Bihan 1 Florent Chatelain 2 Jonathan Manton 3
1 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
2 GIPSA-SAIGA - SAIGA
GIPSA-DA - Département Automatique, GIPSA-DIS - Département Images et Signal
Abstract : This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres S p−1. It allows one to derive the Fourier expansions on S p−1 of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on S p−1 is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on S p−1 are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on S p−1. Index Terms Isotropic random walk on S p−1 , Compound Cox Processes on S p−1 , von Mises-Fisher distribution, Fourier series expansion on hyperspheres, multiple scattering, Cramer-Rao lower bounds.
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Nicolas Le Bihan, Florent Chatelain, Jonathan Manton. Isotropic Multiple Scattering Processes on Hyperspheres. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2016, 62 (10), pp.5740-5752. ⟨10.1109/TIT.2015.2508932⟩. ⟨hal-01322340⟩

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