Title :
Balanced GHM-like multiscaling functions
Author :
Selesnick, Ivan W.
Author_Institution :
Dept. of Electr. Eng., Polytech. Univ., Brooklyn, NY, USA
fDate :
5/1/1999 12:00:00 AM
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;
Journal_Title :
Signal Processing Letters, IEEE
