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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Bibliographic Details
Main Authors: Yeon Ju Lee, Jungho Yoon
Format: Article
Language:English
Published: Wiley 2011-01-01
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.
ISSN:1085-3375
1687-0409