Radial 3D-Needlets on the Unit Ball. Issue Volume 10:Issue S306(2014) (1st July 2015)

• Record Type: Journal Article
• Authors: Durastanti, Claudio; Fantaye, Yabebal T.; Hansen, Frode K.; Marinucci, Domenico; Pesenson, Isaac Z.
• Editors: Heavens, A. F.; Starck, J.-L.; Krone-Martins, A.
• Is Part Of: Proceedings of the International Astronomical Union. Volume 10:Issue S306(2014)
• Page Start: 75
• Page End: 77
• Publication Date: 2015-07-01
• Subjects: methods: data analysis, -- methods: statistical, -- cosmology: observations; Astronomy -- Congresses; Astronomy -- Periodicals; 520
• DOI: 10.1017/S1743921314010801
• Languages: English
• ISSNs: 1743-9213

Abstract

Abstract: 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.