Bispectral techniques for spherical functions

The authors address two problems involving spherical functions: determining when two spherical functions are 3-D rotated copies of each other; and averaging several noisy observations of a rotating spherical function. The solution to both problems uses the spherical bispectrum, which is the generalization of the well-known Euclidean bispectrum. The spherical bispectrum is formulated and it is shown that it is invariant under 3-D rotation of the underlying Gaussian noise. An algorithm for recovering spherical functions from their bispectra is demonstrated.<>