An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms

@article{Khalid2014AnOS,
  title={An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms},
  author={Zubair Khalid and Rodney A. Kennedy and Jason D. McEwen},
  journal={IEEE Transactions on Signal Processing},
  year={2014},
  volume={62},
  pages={4597-4610}
}
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L2 samples. We obtain the optimal number of samples given by the degrees of freedom of the signal in harmonic space. The number of samples required in our scheme is a factor of two or four fewer than existing techniques, which require either 2L2 or 4L2 samples. We note, however, that we do not recover a sampling theorem on the… CONTINUE READING
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