Multivariate tight wavelet frames with few generators and high vanishing moments

Youngmi Hur, Zachary Lubberts, Kasso A. Okoudjou

Research output: Contribution to journalArticlepeer-review

Abstract

Tight wavelet frames (TWFs) are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further develop existing work combining sums of squares representations with TWF construction, and present a new and general method for constructing such frames. Focusing on the case of box splines, we also demonstrate how the flexibility of our approach can lead to TWFs with high numbers of vanishing moments for all of the wavelet masks, while still having few highpass masks: in fact, we match the best known upper bound on the number of highpass masks for general box spline TWF constructions, while typically achieving much better vanishing moments for all of the wavelet masks, proving a nontrivial lower bound on this quantity.

Original languageEnglish
Article number2250009
JournalInternational Journal of Wavelets, Multiresolution and Information Processing
DOIs
Publication statusAccepted/In press - 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Information Systems
  • Applied Mathematics

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