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Radial 3D-Needlets on the Unit Ball

Published online by Cambridge University Press:  01 July 2015

Claudio Durastanti ,
Yabebal T. Fantaye ,
Frode K. Hansen ,
Domenico Marinucci  and
Isaac Z. Pesenson
Claudio Durastanti
Affiliation:
Department of Mathematics, University of Tor Vergata, Rome, email: durastan@mat.uniroma2.it
Yabebal T. Fantaye
Affiliation:
Department of Mathematics, University of Tor Vergata, Rome, email: fantaye@mat.uniroma2.it
Frode K. Hansen
Affiliation:
Institutt for teoretisk astrofysikk, University of Oslo, email: f.k.hansen@astro.uio.no
Domenico Marinucci
Affiliation:
Department of Mathematics, University of Tor Vergata, Rome, email: marinucc@mat.uniroma2.it
Isaac Z. Pesenson
Affiliation:
Department of Mathematics, Temple University, Philadelphia, email: isaak.pesenson@temple.edu
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Abstract

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We present a simple construction of spherical wavelets for the unit ball, which we label Radial 3D Needlets. We envisage an experimental framework where data are collected on concentric spheres with the same pixelization at different radial distances from the origin. The unit ball is hence viewed as a tensor product of the unit interval with the unit sphere: a set of eigenfunctions is therefore defined on the corresponding Laplacian operator. Wavelets are then constructed by a smooth convolution of the projectors defined by these eigenfunctions. Localization properties may be rigorously shown to hold in the real and harmonic domain, and an exact reconstruction formula holds; the system allows a very convenient computational implementation.

Keywords

methods: data analysismethods: statisticalcosmology: observations
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 10 , Symposium S306: Statistical Challenges in 21st Century Cosmology , May 2014 , pp. 75 - 77
Copyright
Copyright © International Astronomical Union 2015 

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