Smooth wavelet frames with application to denoising

Ivan W. Selesnick, Levent Şendur

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers the design and application of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grobner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-Tree DWT of Kingsbury (see Proceedings of the Eighth IEEE DSP Workshop, Utah, 1998, and Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Phoenix, 1999), one goal is to keep the redundancy-factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift-invariant). For the tight frame presented here, optimal-Tree based denoising algorithms can be directly applied.

Original languageEnglish (US)
Title of host publicationSignal Processing Theory and Methods I
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages129-132
Number of pages4
ISBN (Electronic)0780362934
DOIs
StatePublished - 2000
Event25th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2000 - Istanbul, Turkey
Duration: Jun 5 2000Jun 9 2000

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume1
ISSN (Print)1520-6149

Conference

Conference25th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2000
CountryTurkey
CityIstanbul
Period6/5/006/9/00

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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  • Cite this

    Selesnick, I. W., & Şendur, L. (2000). Smooth wavelet frames with application to denoising. In Signal Processing Theory and Methods I (pp. 129-132). [861887] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 1). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2000.861887