On extensions of wavelet systems to dual pairs of frames

Ole Christensen, Hong Oh Kim, Rae Young Kim

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalAdvances in Computational Mathematics
Issue number2
Pages (from-to)489-503
Publication statusPublished - 2015


  • Bessel sequences
  • Dual frame pairs
  • Wavelet systems


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