Interpolating orthogonal bases of n-separate MRAs and wavelets

E. A. Pleshcheva

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 154-163

Résumé

Interpolating orthogonal wavelet bases are constructed with the use of several scaling functions. In the classical case, a basis of the space ${L}^2(\mathbb{R})$ is formed by shifts and compressions of a single function $\psi$. In contrast to the classical case, we consider several bases of the space $L^2(\mathbb{R})$, which are formed by shifts and compressions of $n$ functions $\psi^s$, $s=1,\ldots,n$. The $n$-separate wavelets constructed by the author earlier form $n$ orthonormal bases of the space $L^2(\mathbb{R})$. In 2008, Yu.Ṅ. Subbotin and N. I. Chernykh suggested a method for modifying the Meyer scaling function in such a way that the basis formed by it is simultaneously orthogonal and interpolating. In the present paper we propose a method for modifying the masks of $n$-separate scaling functions from a wide class in such a way that the resulting new scaling functions and wavelets remain orthogonal and at the same time become interpolating.

Détail

Keywords: orthogonal wavelet, interpolating wavelet, scaling function, basis, multiresolution analysis, mask of a scaling function, $n$-separate wavelet.