Wavelets, ridgelets and curvelets on the sphere
arXiv:astro-ph/0509883 · doi:10.1051/0004-6361:20053246
Abstract
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be inverted i.e. we can exactly reconstruct the original data from its coefficients in either representation. Several applications are described. We show how these transforms can be used in denoising and especially in a Combined Filtering Method, which uses both the wavelet and the curvelet transforms, thus benefiting from the advantages of both transforms. An application to component separation from multichannel data mapped to the sphere is also described in which we take advantage of moving to a wavelet representation.
Accepted for publication in A&A. Manuscript with all figures can be downloaded at http://jstarck.free.fr/aa_sphere05.pdf
References in corpus (3)
Cited by in corpus (79)
- Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
- Directly Observing the Galaxies Likely Responsible for Reionization
- Planck 2013 results. XXV. Searches for cosmic strings and other topological defects
- A full sky, low foreground, high resolution CMB map from WMAP
- Spherical Needlets for CMB Data Analysis
- Full-Sky Weak Lensing Simulation with 70 Billion Particles
- Exact reconstruction with directional wavelets on the sphere
- A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
- Discovery of Magnetic Fields Along Stacked Cosmic Filaments as Revealed by Radio and X-Ray Emission
- Needlet Detection of Features in WMAP CMB Sky and the Impact on Anisotropies and Hemispherical Asymmetries
- Sparsity and adaptivity for the blind separation of partially correlated sources
- CMB data analysis and sparsity
- Exact Wavelets on the Ball
- An Optimal-Dimensionality Sampling Scheme on the Sphere with Fast Spherical Harmonic Transforms
- S2LET: A code to perform fast wavelet analysis on the sphere
- Sparse component separation for accurate CMB map estimation
- Localisation of directional scale-discretised wavelets on the sphere
- Simulating full-sky interferometric observations
- Subsampling needlet coefficients on the sphere
- Hunting for giant cells in deep stellar convective zones using wavelet analysis
- Sardinia Radio Telescope wide-band spectral-polarimetric observations of the galaxy cluster 3C 129
- Second-Generation Curvelets on the Sphere
- Poisson Denoising on the Sphere: Application to the Fermi Gamma Ray Space Telescope
- Spherical 3D Isotropic Wavelets
- Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
- Polarized accretion shocks from the cosmic web
- On the computation of directional scale-discretized wavelet transforms on the sphere
- Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets
- Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
- Directional spin wavelets on the sphere
- Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
- Planck intermediate results. XXXVIII. E- and B-modes of dust polarization from the magnetized filamentary structure of the interstellar medium
- New Approaches to Probing Minkowski Functionals
- Weak lensing mass reconstruction using sparsity and a Gaussian random field
- Analyzing the Gamma-ray Sky with Wavelets
- SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
- Image deconvolution and PSF reconstruction with STARRED: a wavelet-based two-channel method optimized for light-curve extraction
- Quantum Energy Regression using Scattering Transforms
- A hybrid approach to CMB lensing reconstruction on all-sky intensity maps
- Polarized wavelets and curvelets on the sphere
- A Simple Proposal for Radial 3D Needlets
- Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere
- A comparative analysis of denoising algorithms for extragalactic imaging surveys
- Towards a full CDM map-based analysis for weak lensing surveys
- Sparse image reconstruction on the sphere: analysis and synthesis
- 3D weak lensing with spin wavelets on the ball
- Wavelet analysis of baryon acoustic structures in the galaxy distribution
- Wavelet-Based Techniques for the Gamma-Ray Sky
- WMAP 9-year CMB estimation using sparsity
- Fast directional spatially localized spherical harmonic transform
- Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude-Longitude Spatial Region
- Multichannel Poisson denoising and deconvolution on the sphere : Application to the Fermi Gamma Ray Space Telescope
- Data compression on the sphere
- Needatool: A Needlet Analysis Tool for Cosmological Data Processing
- Covariant polarized radiative transfer on cosmological scales for investigating large-scale magnetic field structures
- Testing the isotropy of high energy cosmic rays using spherical needlets
- Wavelet-Based Segmentation on the Sphere
- Sparse point-source removal for full-sky CMB experiments: application to WMAP 9-year data
- CMB map restoration
- Optimal Arrays for Compressed Sensing in Snapshot-Mode Radio Interferometry
- Multiresolution on n-dimensional spheres
- 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
- Directional wavelets on -dimensional spheres
- Joint deconvolution and unsupervised source separation for data on the sphere
- An ultra-high-resolution map of (dark) matter
- Reconstruction of weak lensing mass maps for non-Gaussian studies in the celestial sphere
- TDCOSMO: XX. WFI2033--4723, the First Quadruply-Imaged Quasar Modeled with JWST Imaging
- Spatial-Slepian Transform on the Sphere
- Tail Behaviour of Mexican Needlets
- Polarized CMB recovery with sparse component separation
- Joint SO(3)-Spectral Domain Filtering of Spherical Signals in the Presence of Anisotropic Noise
- Density estimation on the rotation group using diffusive wavelets
- Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
- Learning sparse representations on the sphere
- Estimating fiber orientation distribution from diffusion MRI with spherical needlets
- Joint deconvolution and blind source separation on the sphere with an application to radio-astronomy
- Scale-discretised ridgelet transform on the sphere