Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines | Zendy

KyungYil Lee | Zendy; Jungho Yoon | Zendy

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Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines

Author(s) -

KyungYil Lee,

Jungho Yoon

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/593436

Subject(s) - biorthogonal system , mathematics , wavelet , exponential function , stability (learning theory) , context (archaeology) , polynomial , pure mathematics , biorthogonal wavelet , mathematical analysis , wavelet transform , computer science , biology , paleontology , artificial intelligence , machine learning

This paper is concerned with analyzing the mathematical properties, such as theregularity 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 sameregularities as the ones based on the polynomial B-splines of the corresponding orders. In thecontext of nonstationary wavelets, the stability of wavelet bases is not implied by the stability ofa refinable function. For this reason, we prove that the suggested nonstationary wavelets formRiesz bases for the space that they generate

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