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

Title
On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle
Author(s)
김래영Ole Christensen[Ole Christensen]김홍오[김홍오]
Keywords
HIGH VANISHING MOMENTS; AFFINE SYSTEMS; TIGHT FRAMES; L-2(R-D); MASKS
Issue Date
201406
Publisher
CANADIAN MATHEMATICAL SOC
Citation
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, v.57, no.2, pp.254 - 263
Abstract
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.
URI
http://hdl.handle.net/YU.REPOSITORY/32004http://dx.doi.org/10.4153/CMB-2013-015-9
ISSN
0008-4395
Appears in Collections:
이과대학 > 수학과 > Articles
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