Density estimation on the rotation group using diffusive wavelets

Abstract

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an existing technique using the De La Vallée Poussin kernel estimator. The heat-kernel wavelet approach appears to offer the best convergence, with faster convergence to the optimal bound and guaranteed positivity of the estimated probability density function.

References in corpus (4)

• Wavelets, ridgelets and curvelets on the sphere
• Diffusive wavelets on groups and homogeneous spaces
• Decompounding on compact Lie groups
• Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering

Cited by in corpus (1)

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