Wavelet analysis on some surfaces of revolution via area preserving projection
type: Item
instance of: scholarly article
title: Wavelet analysis on some surfaces of revolution via area preserving projection
zbMATH Open document ID: 1213.42155
published in: Applied and Computational Harmonic Analysis
publication date: 2011-03-09T00:00:00Z
review text: Let \(\mathcal{M}\) be a surface of revolution such that \(\mathcal{M}\) is generated by a smooth curve with infinite length rotating along the \(z\)-axis. Using a simple idea, the author constructs in section 2.1 an area-preserving projection from \(\mathcal{M}\) to (a subset of) the plane \(\mathbb{R}^2\). Three concrete examples are given with an explicit expression of the projection in sections 2.2, 2.3, and 2.4 for the paraboloid, hyperboloid, and conical surface, respectively. Due to the area preserving property of the projection, now any wavelet on the plane \(\mathbb{R}^2\) can be straightforwardly transformed into a corresponding wavelet on the surface \(\mathcal{M}\) of revolution. Consequently, this paper provides a simple way for constructing wavelets on surfaces of revolution generated by a smooth curve with infinite length.
reviewed by: Bin Han
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5862782
zbMATH Keywords: continuous wavelet transform
zbMATH Keywords: discrete wavelet transform
zbMATH Keywords: wavelet transform on manifold
zbMATH Keywords: area-preserving projection
zbMATH Keywords: surface of revolution
author: Daniela Roşca
MaRDI profile type: Publication
full work available at URL: j.acha.2010.09.008
OpenAlex ID: W2030917547
cites work: Q4821607
cites work: THE CONTINUOUS WAVELET TRANSFORM ON CONIC SECTIONS
cites work: Wavelet transform on manifolds: old and new approaches
cites work: Continuous wavelet transform on the hyperboloid
cites work: Sampling theorem and discrete Fourier transform on the hyperboloid
cites work: Wavelets. Theory and applications
cites work: Q3135829
DOI: 10.1016/J.ACHA.2010.09.008
description: scientific article; zbMATH DE number 5862782