Unified approach for constructing multiwavelets with approximation order using refinable super-functions

Abstract

A unified approach for constructing a large class of multiwavelets is presented. This class includes Geronimo-Hardin-Massopust, Alpert, finite element and Daubechies-like multiwavelets. The approach is based on the characterisation of approximation order of r multiscaling functions using a known compactly supported refinable super-function. The characterisation is formulated as a generalised eigenvalue equation. The generalised left eigenvectors of the finite down-sampled convolution matrix L-f give the coefficients in the finite linear combination of multiscaling functions that produce the desired super-function. The unified approach based on the super-function theory can be used to construct new multiwavelets with short support, high approximation order and symmetry.