Aliasing Effects for Samples of Spin Random Fields on the Sphere

TL;DR

This paper analyzes aliasing effects in the reconstruction of spin spherical random fields from discrete samples, identifying alias locations, intensities, and conditions for alias-free reconstruction.

Contribution

It characterizes aliasing in spin spherical fields, determines alias locations and effects, and shows alias-free reconstruction is possible with enough sampling points.

Findings

Aliasing occurs at specific frequency domain locations.

Popular sampling schemes introduce aliasing errors.

Band-limited fields can be reconstructed without aliasing using sufficient samples.

Abstract

This paper investigates aliasing effects emerging from the reconstruction from discrete samples of spin spherical random fields defined on the two-dimensional sphere. We determine the location in the frequency domain and the intensity of the aliases of the harmonic coefficients in the Fourier decomposition of the spin random field and evaluate the consequences of aliasing errors in the angular power spectrum when the samples of the random field are obtained by using some very popular sampling procedures on the sphere, the equiangular and the Gauss-Jacobi sampling schemes. Finally, we demonstrate that band-limited spin random fields are free from aliases, provided that a sufficiently large number of nodes is used in the selected quadrature rule.