An Optimal-Dimensionality Sampling for Spin-s Functions on the Sphere

作者：Elahi Usama^*; Khalid Zubair; Kennedy Rodney A; McEwen Jason D

来源：IEEE Signal Processing Letters, 2018, 25(10): 1470-1474.

DOI：10.1109/LSP.2018.2865676

• Harmonic analysis
• sampling
• sphere
• spherical harmonics
• spin-s functions

For the representation of spin-s band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require similar to 2L(2) samples for the representation of spin-s functions band-limited at L, the proposed scheme requires N-0 = L-2 - s(2) samples for the accurate computation of the spin-s spherical harmonic transform (s-SHT). For the proposed sampling scheme, we also develop a method to compute the s-SHT. We place the samples in our design scheme such that the matrices involved in the computation of s-SHT are well-conditioned. We also present a multipass s-SHT to improve the accuracy of the transform. We also show the proposed sampling design exhibits superior geometrical properties compared to existing equiangular and Causs-Legendre sampling schemes, and enables accurate computation of the s-SHT corroborated through numerical experiments.

• 出版日期2018-10