Recently we found a family of nearly orthonormal affine Riesz bases of compact support and arbitrary degrees of smoothness, obtained by perturbing the onedimensional Haar mother wavelet using B-splines. The mother wavelets thus obtained are symmetric and given in closed form, features which are gene
Riesz wavelets and generalized multiresolution analyses
β Scribed by Marcin Bownik
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 145 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1063-5203
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β¦ Synopsis
We investigate Riesz wavelets in the context of generalized multiresolution analysis (GMRA). In particular, we show that Zalik's class of Riesz wavelets obtained by an MRA is the same as the class of biorthogonal wavelets associated with an MRA.
π SIMILAR VOLUMES
The paper presents a general approach to the construction of so-called biorthogonal vector-MRA and its related wavelets of L 2 (R d ). The presented algorithm is very close to the one in the classical case given by Cohen-Daubechies (d Γ 1) and Long-Chen (d Β§ 1). Roughly speaking, to get a biorthogon
We first characterize the Riesz wavelets which are associated with multiresolution analyses (MRAs) and the Riesz wavelets whose duals are also Riesz wavelets. The characterizations show that if a Riesz wavelet is associated with an MRA, then it has a dual Riesz wavelet. We then improve Wang's charac
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