A Simple Proposal for Radial 3D Needlets
arXiv:1408.1095 · doi:10.1103/PhysRevD.90.103532
Abstract
We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre of the ball is surrounded by concentric spheres with the same pixelization at different radial distances, for any given resolution. The system is then obtained by weighting the projector operator built on the corresponding set of eigenfunctions, and performing a discretization step which turns out to be computationally very convenient. The resulting wavelets can be shown to have very good localization properties in the real and harmonic domain; their implementation is computationally very convenient, and they allow for exact reconstruction as they form a tight frame systems. Our theoretical results are supported by an extensive numerical analysis.
12 pages, 4 figure panels, submitted to PRD
References in corpus (36)
- HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
- Simulating the joint evolution of quasars, galaxies and their large-scale distribution
- Efficient Computation of CMB anisotropies in closed FRW models
- Detection of B-mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope
- A full sky, low foreground, high resolution CMB map from WMAP
- Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope
- Integrated Sachs-Wolfe effect from the cross correlation of WMAP3 year and the NRAO VLA sky survey data: New results and constraints on dark energy
- Spherical Needlets for CMB Data Analysis
- Wavelets, ridgelets and curvelets on the sphere
- Foreground component separation with generalised ILC
- Exact reconstruction with directional wavelets on the sphere
- Asymptotics for spherical needlets
- AGILE detection of GeV gamma-ray emission from the SNR W28
- TeV gamma-ray survey of the Northern sky using the ARGO-YBJ detector
- An Estimate of the Primordial Non-Gaussianity Parameter f_NL Using the Needlet Bispectrum from WMAP
- Continuous Wavelets on Compact Manifolds
- 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
- Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory
- The needlets bispectrum
- Exact Wavelets on the Ball
- S2LET: A code to perform fast wavelet analysis on the sphere
- Sparse component separation for accurate CMB map estimation
- Constraints on f_nl and g_nl from the analysis of the N-pdf of the CMB large scale anisotropies
- Spherical 3D Isotropic Wavelets
- On the linear term correction for needlets/wavelets non-Gaussianity estimators
- Scale dependent non-Gaussianities in the CMB data identified with Minkowski Functionals and Scaling Indices
- Polarized wavelets and curvelets on the sphere
- General CMB bispectrum analysis using wavelets and separable modes
- WMAP 9-year CMB estimation using sparsity
- Multichannel Poisson denoising and deconvolution on the sphere : Application to the Fermi Gamma Ray Space Telescope
- Testing the isotropy of high energy cosmic rays using spherical needlets
- Detection of new point sources in WMAP 7 year data using internal templates and needlets
- Wilkinson Microwave Anisotropy Probe 7-yr constraints on fNL with a fast wavelet estimator
- Neutrino searches with the IceCube telescope
- On the Numerical Evaluation of a Class of Oscillatory Integrals in Worldline Variational Calculations
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- Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs
- Needlet estimation of cross-correlation between CMB lensing maps and LSS
- Aliasing effects for random fields over spheres of arbitrary dimension
- Scale-discretised ridgelet transform on the sphere
- Bayesian variational regularization on the ball