On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle

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The unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.
Publisher
CANADIAN MATHEMATICAL SOC
Issue Date
2014-06
Language
English
Article Type
Article
Keywords

HIGH VANISHING MOMENTS; AFFINE SYSTEMS; TIGHT FRAMES; L-2(R-D); MASKS

Citation

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, v.57, no.2, pp.254 - 263

ISSN
0008-4395
DOI
10.4153/CMB-2013-015-9
URI
http://hdl.handle.net/10203/189278
Appears in Collection
MA-Journal Papers(저널논문)
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