Construction of Bivariate Nonseparable Compactly Supported Orthogonal Wavelets

摘要

A method for constructing bivariate nonseparable compactly supported orthogonal scaling functions, and the corresponding wavelets, using the dilation matrix M := 2~nI = 2~n [1001], (d = detM = 2~(2n) ≥ 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 m_0(ω), to be used in our method. There follows that the wavelets can be made arbitrarily smooth by properly choosing the accuracy parameter r.