We present here a simple construction of a wavelet system for the three-dimensional ball, which we label radial 3D needlets. The construction envisages a data collection environment in which an observer located at the center of the ball is surrounded by concentric spheres with the same pixelization at different radial distances, for any given resolution. The system is then obtained by weighting the projector operator built on the corresponding set of eigenfunctions and performing a discretization step which turns out to be computationally very convenient. The resulting wavelets can be shown to have very good localization properties in the real and harmonic domain; their implementation is computationally very convenient, and they allow for exact reconstruction as they form a tight frame system. Our theoretical results are supported by an extensive numerical analysis.

Durastanti, C., Fantaye, Y., Hansen, F., Marinucci, D., Pesenson, I. (2014). Simple proposal for radial 3D needlets. PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY, 90(10), 103532 [10.1103/PhysRevD.90.103532].

Simple proposal for radial 3D needlets

MARINUCCI, DOMENICO;
2014-01-01

Abstract

We present here a simple construction of a wavelet system for the three-dimensional ball, which we label radial 3D needlets. The construction envisages a data collection environment in which an observer located at the center of the ball is surrounded by concentric spheres with the same pixelization at different radial distances, for any given resolution. The system is then obtained by weighting the projector operator built on the corresponding set of eigenfunctions and performing a discretization step which turns out to be computationally very convenient. The resulting wavelets can be shown to have very good localization properties in the real and harmonic domain; their implementation is computationally very convenient, and they allow for exact reconstruction as they form a tight frame system. Our theoretical results are supported by an extensive numerical analysis.
2014
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
Settore FIS/05 - ASTRONOMIA E ASTROFISICA
English
Durastanti, C., Fantaye, Y., Hansen, F., Marinucci, D., Pesenson, I. (2014). Simple proposal for radial 3D needlets. PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY, 90(10), 103532 [10.1103/PhysRevD.90.103532].
Durastanti, C; Fantaye, Y; Hansen, F; Marinucci, D; Pesenson, I
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/131234
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