S2LET: A code to perform fast wavelet analysis on the sphere

Abstract

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals on the sphere. The scale-discretised wavelet transform was developed previously and reduces to the needlet transform in the axisymmetric case. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.

8 pages, 6 figures, version accepted for publication in A&A. Code is publicly available from http://www.s2let.org

References in corpus (18)

• Spherical Needlets for CMB Data Analysis
• Exact reconstruction with directional wavelets on the sphere
• Asymptotics for spherical needlets
• Detection of the ISW effect and corresponding dark energy constraints
• Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets
• Libsharp - spherical harmonic transforms revisited
• Global universe anisotropy probed by the alignment of structures in the cosmic microwave background
• Needlet Detection of Features in WMAP CMB Sky and the Impact on Anisotropies and Hemispherical Asymmetries
• Cosmological applications of a wavelet analysis on the sphere
• The needlets bispectrum
• Exact Wavelets on the Ball
• Alignment and signed-intensity anomalies in WMAP data
• Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures
• Complex data processing: fast wavelet analysis on the sphere
• Libpsht - algorithms for efficient spherical harmonic transforms
• Non-Gaussianity analysis on local morphological measures of WMAP data
• Steerable wavelet analysis of CMB structures alignment
• Polarized wavelets and curvelets on the sphere

Cited by in corpus (33)

• Localisation of directional scale-discretised wavelets on the sphere
• Second-Generation Curvelets on the Sphere
• On the computation of directional scale-discretized wavelet transforms on the sphere
• Directional spin wavelets on the sphere
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
• Non-Gaussian modelling and statistical denoising of Planck dust polarization full-sky maps using scattering transforms
• The Atacama Cosmology Telescope: Map-Based Noise Simulations for DR6
• SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
• A Simple Proposal for Radial 3D Needlets
• Spin-SILC: CMB polarisation component separation with spin wavelets
• 3D weak lensing with spin wavelets on the ball
• Sparse image reconstruction on the sphere: analysis and synthesis
• Fourier-Laguerre transform, convolution and wavelets on the ball
• Dark Matter Distribution Induced by a Cosmic String Wake in the Nonlinear Regime
• Mapping dark matter on the celestial sphere with weak gravitational lensing
• Covariant polarized radiative transfer on cosmological scales for investigating large-scale magnetic field structures
• A Novel CMB Component Separation Method: Hierarchical Generalized Morphological Component Analysis
• Differentiable and accelerated spherical harmonic and Wigner transforms
• Generative models of astrophysical fields with scattering transforms on the sphere
• Posterior sampling for inverse imaging problems on the sphere in seismology and cosmology
• Wavelet-Based Segmentation on the Sphere
• Slepian Scale-Discretised Wavelets on the Sphere
• Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs
• Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
• Flaglets for studying the large-scale structure of the Universe
• A Note on Spherical Needlets
• Analysing the polarisation of the CMB with spin scale-discretised wavelets
• Flaglets: Exact Wavelets on the Ball
• SLEPLET: Slepian Scale-Discretised Wavelets in Python
• Scale-discretised ridgelet transform on the sphere
• Bayesian variational regularization on the ball