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.
On Riesz wavelets associated with multiresolution analyses
โ Scribed by Hong Oh Kim; Rae Young Kim; Yong Hoon Lee; Jae Kun Lim
- Book ID
- 108485511
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 167 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1063-5203
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๐ SIMILAR VOLUMES
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
We present some necessary and sufficient conditions for a frame multiresolution analysis (FMRA) to admit a frame wavelet whose dyadic dilations and integer translates generate a frame for L 2 (R) and propose a construction of a wavelet, if it exists, which reduces to the classical orthonormal wavele