mlsanityData to 7 Oct 2026

Near Optimal Reconstruction of Spherical Harmonic Expansions

arXiv 2202.12995 ↗First posted 25 Feb 2022math.NA cs.DS cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere mathbbSd-1 using a near-optimal number of function evaluations. We show that for any f ∈ L2(mathbbSd-1), the number of evaluations of f needed to recover its degree-q spherical harmonic expansion equals the dimension of the space of spherical harmonics of degree at most q up to a logarithmic factor. Moreover, we develop a simple yet efficient algorithm to recover degree-q expansion of f by only evaluating the function on uniformly sampled points on mathbbSd-1. Our algorithm is based on the connections between spherical harmonics and Gegenbauer polynomials and leverage score sampling methods. Unlike the prior results on fast spherical harmonic transform, our proposed algorithm works efficiently using a nearly optimal number of samples in any dimension d. We further illustrate the empirical performance of our algorithm on numerical examples.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 12 of its 37 references that are in the map. First posted on arXiv 25 Feb 2022.

Builds on

12 of 37 references.

References · 12

  1. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  2. 2019Linearized two-layers neural networks in high dimensioncited by 155
  3. 2018Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guaranteescited by 71
  4. 2017Active Regression via Linear-Sample Sparsificationcited by 36
  5. 2021Scaling Neural Tangent Kernels via Sketching and Random Featurescited by 32
  6. 2022Equivariance versus Augmentation for Spherical Imagescited by 24
  7. 2020Fourier Sparse Leverage Scores and Approximate Kernel Learningcited by 16
  8. 2018A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transformscited by 13
  9. 2022Random Gegenbauer Features for Scalable Kernel Methodscited by 6
  10. 2022Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Timecited by 6
  11. 2016Fourier-sparse interpolation without a frequency gapcited by 5
  12. 2019Dimension-independent Sparse Fourier Transformcited by 2

Built on by

Not cited yet.