Related papers: Spin Wavelets on the Sphere
The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets…
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 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…
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 construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
Compared with the traditional spherical harmonics, the spherical needlets are a new generation of spherical wavelets that possess several attractive properties. Their double localization in both spatial and frequency domains empowers them…
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 consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere (Mexican needlets) which were recently introduced in the literature by Geller and Mayeli (2007). We provide necessary and…
We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools…
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than…
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 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…
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 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…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the…
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…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…