Related papers: Correspondence principle between spherical and Euc…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…
A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
We discuss a new scale-discretised directional wavelet transform to analyse spin signals defined on the sphere, in particular the polarisation of the cosmic microwave background (CMB).
This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
Observations of the Cosmic Microwave Background (CMB) provide increasingly accurate information about the structure of the Universe at the recombination epoch. Most of this information is encoded in the angular power spectrum of the CMB.…
The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem…
We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
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…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of…
In cosmic-ray physics, large field of view experiments are triggered by a number of signals laying on different angular scales: point-like and extended gamma-ray sources, diffuse emissions, as well as large and intermediate scale cosmic-ray…
Fundamental information about the Universe is encoded in anisotropies of the Cosmic Microwave Background (CMB) radiation. To make full use of this information, an experiment must image the entire sky with the angular resolution,…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…