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Kim, Hongoh
Division of General Studies
Research Interests
  • Complex Analysis
  • Harmonic Analysis
  • Wavewlets and Gabor Systems

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On extensions of wavelet systems to dual pairs of frames

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Title
On extensions of wavelet systems to dual pairs of frames
Author
Christensen, OleKim, HongohKim, Rae Young
Issue Date
2016-04
Publisher
SPRINGER
Citation
ADVANCES IN COMPUTATIONAL MATHEMATICS, v.42, no.2, pp.489 - 503
Abstract
It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems are generated by the multiscale setup with trigonometric masks and provide a positive answer under extra assumptions. We also identify a number of conditions that are necessary for the extension to dual (multi-) wavelet frames with any number of generators, and show that they imply that an extension with two pairs of wavelet systems is possible. Along the way we provide examples that demonstrate the extra flexibility in the extension to dual pairs of frames compared with the more popular extensions to tight frames.
URI
https://scholarworks.unist.ac.kr/handle/201301/17914
URL
http://link.springer.com/article/10.1007%2Fs10444-015-9432-1
DOI
10.1007/s10444-015-9432-1
ISSN
1019-7168
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PHY_Journal Papers
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