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Titolo:
An algebraic structure of orthogonal wavelet space
Autore:
Tian, J; Wells, RO;
Indirizzi:
Digimarc Corp, Tualatin, OR 97062 USA Digimarc Corp Tualatin OR USA 97062Digimarc Corp, Tualatin, OR 97062 USA Int Univ, Bremen, Germany Int Univ Bremen GermanyInt Univ, Bremen, Germany
Titolo Testata:
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
fascicolo: 3, volume: 8, anno: 2000,
pagine: 223 - 248
SICI:
1063-5203(200005)8:3<223:AASOOW>2.0.ZU;2-Q
Fonte:
ISI
Lingua:
ENG
Soggetto:
FILTER BANKS; DESIGN; BASES;
Keywords:
wavelets; parameterization; fast implementation;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Engineering, Computing & Technology
Citazioni:
40
Recensione:
Indirizzi per estratti:
Indirizzo: Tian, J Digimarc Corp, Tualatin, OR 97062 USA Digimarc Corp Tualatin OR USA 97062 Corp, Tualatin, OR 97062 USA
Citazione:
J. Tian e R.O. Wells, "An algebraic structure of orthogonal wavelet space", AP COMP HAR, 8(3), 2000, pp. 223-248

Abstract

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parameterization of wavelet space, one can define a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus g to the (g - 1) dimensional real torus (the products of unit circles). By the uniqueness and erectness of factorization, this mapping is well defined and one-to-one. Thus we can equip the rank 2 orthogonal wavelet space with an algebraic structure of the torus. Because of the degenerate phenomenon of the paraunitary matrix, the parameterization map is not onto. However, there exists an ontomapping from the torus to the closure of the wavelet space. And with such mapping, a more complete parameterization is obtained. By utilizing the factorization theory, we present a fast implementation of discrete wavelet transform (DWT). In general, the computational complexity of a rank m orthogonal DWT is O(m(2)g). In this paper we start with a given scaling filter and construct additional (m - 1) wavelet filters so that the DWT can be implemented in O(mg). With a fixed scaling filter, the approximation order, the orthogonality, and the smoothness remain unchanged; thus our fast DWT implementation is guile general. (C) 2000 Academic Press.

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Documento generato il 06/07/20 alle ore 09:00:52