A study of orthonormal multi-wavelets Original Research Article

A general scheme for constructing symmetric and/or antisymmetric compactly supported orthonormal multi-scaling functions and multi-wavelets is introduced. The main emphasis is on maximum order of polynomial-reproduction by the scaling functions, or equivalently maximum number of vanishing moments for the corresponding wavelets; particularly for those that have small supports and those that satisfy certain Hermite interpolating conditions. As an application, we recover the Geronimo-Hardin-Massopust multi-scaling function without using fractal interpolation, and consequently the corresponding Strang-Strela multi-wavelet. Explicit formulations of the two-scale relations and polynomial-reproduction identities for the scaling functions with supports [0,2] and [0,3] and multiplicity 2 as well as their corresponding multi-wavelet are also derived by following our general constructive scheme.