Two-dimensional orthogonal wavelets with vanishing moments

We investigate a very general subset of two-dimensional, orthogonal, compactly supported wavelets. This subset includes all the wavelets with a corresponding wavelet (polyphase) matrix that can be factored as a product of factors of degree-1 in one variable. In this paper we consider in particular wavelets with vanishing moments. The number of vanishing moments that can be achieved increases with the increase of the McMillan degrees of the wavelet matrix. We design wavelets with the maximal number of vanishing moments for given McMillan degrees, by solving a set of nonlinear constraints on the free parameters deening the wavelet matrix, and discuss their relation to regular, smooth wavelets. Design examples are given for two fundamental sampling schemes; the quincunx and the four-band separable sampling. Their relation to the, well known, one-dimensional Daubechies wavelets with vanishing moments is discussed.