Some generalized method for constructing nonseparable compactly supported wavelets in $L^2(R^2)$

In this paper we show some construction of nonseparable compactly supported bivariate wavelets. We deal with the dilation matrix \(A = \tiny{\left[\begin{matrix}0 & 2 \cr 1 & 0 \cr \end{matrix} \right]}\) and some three-row coefficient mask; that is a scaling function satisfies a dilation equation with scaling coefficients which can be contained in the set \(\{c_{n}\}_{n \in\mathcal{S}},\) where \(\mathcal{S}=S_{1} \times \{0,1,2\},\) \(S_{1} \subset \mathbb{N},\) \(\sharp S_{1} \lt \infty.\