Related papers: A needlet-based approach to the full-sky data anal…
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…
We introduce NeedATool (Needlet Analysis Tool), a software for data analysis based on needlets, a wavelet rendition which is powerful for the analysis of fields defined on a sphere. Needlets have been applied successfully to the treatment…
For many decades, ultrahigh energy charged particles of unknown origin that can be observed from the ground have been a puzzle for particle physicists and astrophysicists. As an attempt to discriminate among several possible production…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
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.…
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…
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…
Over the last few years, needlets have a emerged as a useful tool for the analysis of Cosmic Microwave Background (CMB) data. Our aim in this paper is first to introduce in the CMB literature a different form of needlets, known as Mexican…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
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 mathematical literature by Geller and Marinucci…
We apply spherical needlets to the Wilkinson Microwave Anisotropy Probe 5-year cosmic microwave background (CMB) dataset, to search for imprints of non-isotropic features in the CMB sky. We use the needlets localization properties to…
The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation…
In cosmology, the analysis of observational evidence is very important to test theoretical models of the Universe. Artificial neural networks are powerful and versatile computational tools for data modelling and are recently being…
We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional…
We consider wavelets as a tool to perform a variety of tasks in the context of analyzing cosmic microwave background (CMB) maps. Using Spherical Haar Wavelets we define a position and angular-scale-dependent measure of power that can be…
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…
The cosmic microwave background radiation is supposed to be Gaussian and this hypothesis is in good agreement with the recent very accurate measurements. Nonetheless a tiny amount of non-Gaussianity is predicted by the standard inflation…
Making use of the wealth of new observational data coming from the sky it is possible to constrain particle physics theories beyond the Standard Model. One way to do this is illustrated in this article: a subset of theories admits cosmic…
We consider the statistical analysis of random sections of a spin fibre bundle over the sphere. These may be thought of as random fields that at each point p in $S^2$ take as a value a curve (e.g. an ellipse) living in the tangent plane at…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…