Some generalized method for constructing nonseparable compactly supported wavelets in L2(R2)

Abstract

In this paper we show the construction of nonseparable compactly supported bi-variate 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 that satisfies a dilation equation with scaling coefficients which can be contained in the set ${c_{n}}{n \in\mathcal{S}},$ where $\mathcal{S}=S{1} \times {0,1,2},$ $S_{1} \subset \mathbb{N},$ $\sharp S_{1} \lt \infty.$