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arXiv · 1907.13339

Fast Tensor Needlet Transforms for Tangent Vector Fields on the Sphere

Ming Li·Philip Broadbridge·Andriy Olenko·Yu Guang Wang
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Abstract

This paper constructs a semi-discrete tight frame of tensor needlets associated with a quadrature rule for tangent vector fields on the unit sphere $\mathbb{S}^2$ of $\mathbb{R}^3$ --- tensor needlets. The proposed tight tensor needlets provide a multiscale representation of any square integrable tangent vector field on $\mathbb{S}^2$, which leads to a multiresolution analysis (MRA) for the field. From the MRA, we develop fast algorithms for tensor needlet transforms, including the decomposition and reconstruction of the needlet coefficients between levels, via a set of filter banks and scalar FFTs. The fast tensor needlet transforms have near linear computational cost proportional to $N\log \sqrt{N}$ for $N$ evaluation points or coefficients. Numerical examples for the simulated and real data demonstrate the efficiency of the proposed algorithm.

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Ming Li, Philip Broadbridge, Andriy Olenko, Yu Guang Wang. 2019-07-31. Fast Tensor Needlet Transforms for Tangent Vector Fields on the Sphere. https://arxiv.org/abs/1907.13339

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