A Simple Proposal for Radial 3D Needlets
Abstract
We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre 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 systems. Our theoretical results are supported by an extensive numerical analysis.
Keywords
Cite
@article{arxiv.1408.1095,
title = {A Simple Proposal for Radial 3D Needlets},
author = {Claudio Durastanti and Yabebal T. Fantaye and Frode K. Hansen and Domenico Marinucci and Isaac Z. Pesenson},
journal= {arXiv preprint arXiv:1408.1095},
year = {2014}
}
Comments
12 pages, 4 figure panels, submitted to PRD