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

Ole Christensen, Hong Oh Kim, Rae Young Kim

Research output: Contribution to journalJournal articleResearchpeer-review

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.
Original languageEnglish
JournalCanadian Mathematical Bulletin
Volume57
Issue number2
Pages (from-to)254-263
ISSN0008-4395
DOIs
Publication statusPublished - 2014

Keywords

  • MATHEMATICS
  • HIGH VANISHING MOMENTS
  • AFFINE SYSTEMS
  • TIGHT FRAMES
  • L-2(R-D)
  • MASKS
  • Bessel sequences
  • frames
  • extension of wavelet Bessel system to tight frame
  • wavelet systems
  • unitary extension principle

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