2-DIMENSIONAL ORTHOGONAL WAVELETS WITH VANISHING MOMENTS

We investigate a very general subset of 2-D, orthogonal, compactly sup ported wavelets, This subset includes all the wavelets with a correspo nding wavelet (polyphase) matrix that can be factored as a product of factors of degree-1 in one variable. In this paper, we consider, in pa rticular, wavelets with vanishing moments, The number of vanishing mom ents that can be achieved increases with the increase in the McMillan degrees of the wavelet matrix. We design wavelets with the maximal num ber of vanishing moments for given McMillan degrees by solving a set o f nonlinear constraints on the free parameters defining the wavelet ma trix and discuss their relation to regular, smooth wavelets, Design ex amples are given for two fundamental sampling schemes: the quincunx an d the four-band separable sampling, The relation of the wavelets to th e well-known 1-D Daubechies wavelets with vanishing moments is discuss ed.