Balanced GHM-like multiscaling functions

Author

Selesnick, Ivan W.

Author_Institution

Dept. of Electr. Eng., Polytech. Univ., Brooklyn, NY, USA

Volume

6

Issue

5

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

111

Lastpage

112

Abstract

The Geronimo-Bardin-Massopust (see J. Approx. Theory, vol.78, p.373-401, 1994) multiwavelet basis exhibits symmetry, orthogonality, short support, and approximation order K=2, which is not possible for wavelet bases based on a single scaling-wavelet function pair. However, the filterbank associated with this basis does not inherit the zero moment properties of the basis. This work describes a version of the GHM multiscaling functions (constructed with Grobner bases) for which the zero moment properties do carry over to the associated filterbank. That is, the basis is balanced up to its approximation order K=2.

Keywords

approximation theory; channel bank filters; filtering theory; image processing; wavelet transforms; Geronimo-Bardin-Massopust multiwavelet basis; Grobner bases; approximation order; balanced GHM-like multiscaling functions; filterbank; image processing; orthogonality; scaling-wavelet function pair; short support; symmetry; zero moment properties; Discrete wavelet transforms; Filter bank; Finite impulse response filter; Image processing; Nonlinear equations; Polynomials; Signal generators;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/97.755430

Filename

755430