Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines
This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions, and then we show that the re...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/593436 |
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| Summary: | This paper is concerned with analyzing the mathematical properties, such as the
regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines.
We first discuss the biorthogonality condition of the nonstationary refinable functions,
and then we show that the refinable functions based on exponential B-splines have the same
regularities as the ones based on the polynomial B-splines of the corresponding orders. In the
context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of
a refinable function. For this reason, we prove that the suggested nonstationary wavelets form
Riesz bases for the space that they generate. |
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| ISSN: | 1085-3375 1687-0409 |