Balanced GHM-like multiscaling functions
Ivan Selesnick · IEEE Signal Processing Letters · 1999
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.