Opuscula Math. 33, no. 2 (2013), 223-235
http://dx.doi.org/10.7494/OpMath.2013.33.2.223

Opuscula Mathematica

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

Wojciech Banaś

Abstract. 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 $$\mathcal{S}=S_{1} \times \{0,1,2\},$$ $$S_{1} \subset \mathbb{N},$$ $$\sharp S_{1} \lt \infty.$$

Keywords: compactly supported wavelet, compactly supported scaling function, multiresolution analysis, dilation matrix, orthonormality, accuracy.

Mathematics Subject Classification: 42C40.

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• Wojciech Banaś
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
• Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Krakow, Poland
• Revised: 2012-08-16.
• Accepted: 2012-09-13.