Fast and Accurate Spherical Harmonic Transform for Spatio-Temporal Regular Grid Data

We propose a fast and accurate spherical harmonic transform (SHT) to facilitate harmonic analysis of current and forthcoming high-resolution datasets acquired on a regular grid, commonly encountered in a variety of applications including but not limited to, medical imaging, geophysics, and climate studies. In contrast to other methods that take the points on the sphere on a Gaussian grid (non-uniform) or a pre-defined uniform grid parameterized by the band-limit (spectral truncation) of the data, the proposed method computes the SHT of the data available on a grid formed by the arbitrary number of equiangular latitudes and longitudes. Since the number of temporal observations in the spatio-temporal data can be in the millions, we also propose a pre-computation for SHT that does not alter the asymptotic computational complexity but results in a significant reduction in the computation time. Our analysis of accuracy and computation time on both synthetic and real datasets validates the proposed developments. To demonstrate the utility of the proposed method, we implement the spatial isotropy test using the largest eigenvalue of the correlation matrix of harmonic coefficients as a test statistic and demonstrate the superior performance of the proposed method in comparison to least-squares for computing SHT.