Approximately dual pairs of wavelet frames

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This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames {alpha(j/2) psi(alpha(j) . -kb)}(j, k is an element of z) in L-2(R) for which no dual frame has wavelet structure. We first generalize this result by proving that there exist wavelet frames for which no approximately dual frame has wavelet structure. Motivated by this we show that by imposing a very mild decay condition on the Fourier transform of the generator psi is an element of L-2(R), a certain oversampling {alpha(j)(/2) psi(alpha(j) . - kb/N)}(j,)(k is an element of z) indeed has an approximately dual wavelet frame; most importantly, by choosing the parameter N is an element of N sufficiently large we can get as close to perfect reconstruction as desired, which makes the approximate dual frame pairs perform equally well as the classical dual frame pairs in applications. (C) 2021 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2022-03
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.507, no.2

ISSN
0022-247X
DOI
10.1016/j.jmaa.2021.125841
URI
http://hdl.handle.net/10203/295869
Appears in Collection
MA-Journal Papers(저널논문)
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