Construction of Bivariate Nonseparable Compactly Supported Orthogonal Wavelets

Abstract

A method for constructing bivariate nonseparable compactly supported orthogonal scaling functions, and the corresponding wavelets, using the dilation matrixM:=2n𝕀=2n[1001],(d=detM=22n≥4,n∈ℕ)is given. The accuracy and smoothness of the scaling functions are studied, thus showing that they have the same accuracy order as the univariate Daubechies low-pass filterm0(ω), to be used in our method. There follows that the wavelets can be made arbitrarily smooth by properly choosing the accuracy parameterr.