# Fast spin ±2 spherical harmonics transforms and application in cosmology

@article{Wiaux2007FastS, title={Fast spin ±2 spherical harmonics transforms and application in cosmology}, author={Yves Wiaux and Laurent Jacques and Pierre Vandergheynst}, journal={J. Comput. Phys.}, year={2007}, volume={226}, pages={2359-2371} }

## 31 Citations

### FAST AND EXACT SPIN-s SPHERICAL HARMONIC TRANSFORMS

- Physics
- 2010

We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed…

### A Mathematical View on Spin-Weighted Spherical Harmonics and Their Applications in Geodesy

- PhysicsMathematische Geodäsie/Mathematical Geodesy
- 2020

The spin-weighted spherical harmonics (by Newman and Penrose) form an orthonormal basis of L2(Ω) on the unit sphere Ω and have a huge field of applications. Mainly, they are used in quantum mechanics…

### A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

- PhysicsJ. Comput. Phys.
- 2013

### A Novel Sampling Theorem on the Sphere

- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 2011

This work develops a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension and highlights the advantages of the sampling theorem in the context of potential applications, notably in the field of compressive sampling.

### A Novel Sampling Theorem on the Rotation Group

- Computer Science, MathematicsIEEE Signal Processing Letters
- 2015

A novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) is developed by connecting the rotation group to theThree-torus through a periodic extension, and fast algorithms to compute the associated Fourier transform are presented.

### A Unified Approach to Scalar, Vector, and Tensor Slepian Functions on the Sphere and Their Construction by a Commuting Operator

- MathematicsAnalysis and Applications
- 2022

Linear relationships between the spin-weighted and the classical scalar, vectorial, tensorial, and higher-rank spherical harmonics allow the construction of classical spherical-harmonic-based Slepian functions from their spin- Weighted counterparts, effectively rendering theConstruction of spherical-cap SlePian functions for any tensorial rank a computationally fast and numerically stable task.

### Spin Needlets for Cosmic Microwave Background Polarization Data Analysis

- Physics
- 2008

Scalar wavelets have been used extensively in the analysis of cosmic microwave background (CMB) temperature maps. Spin needlets are a new form of (spin) wavelets which were introduced in the…

### An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms

- MathematicsIEEE Transactions on Signal Processing
- 2014

We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L2 samples. We obtain the…

### Improving the spatial dimensionality of Gauss-Legendre and equiangular sampling schemes on the sphere

- Mathematics2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2017

An efficient GL sampling scheme with spatial dimensionality equal to that of equiangular scheme is proposed and it is demonstrated that the accuracy of the SHT is not affected with the proposed reduction in the spatialdimensionality.

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