Construction of Bivariate Nonseparable Compactly Supported Orthogonal Wavelets

Abstract EN

A method for constructing bivariate nonseparable compactly supported orthogonal scaling functions, and the corresponding wavelets, using the dilation matrix M:=2n?=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 filter m0(ω), to be used in our method.

There follows that the wavelets can be made arbitrarily smooth by properly choosing the accuracy parameter r.