Basis selection for wavelet processing of sparse source signals

Ian Atkinson, Farzad Kamalabadi

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

Abstract

An attractive property of wavelet bases is their ability to sparsely represent piecewise polynomial signals. The sparsity of a waveletdomain representation depends on several factors such as the mother wavelet, the number of decomposition levels, and the structure of the original signal. We consider the problem of selecting an overcomplete or dyadic wavelet basis that can sparsely represent a sparse piecewise polynomial signal. Most exisisting applicadons that apply wavelet-domain processing techniques to signals that are inherently sparse have not considered the sparsity of underlying signal when selecting a wavelet basis. By accounting for the initial sparseness of a signal, the maximum wavelet filter length and number of decomposition levels can be computed. Selecting a wavelet basis that satisfies these maximum values guarantees that the resulting wavelet-domain representation will be at least as sparse as the original signal. This criteria for wavelet basis selection is of use in applicadons having sparse source signals.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
DOIs
StatePublished - Aug 6 2007
Event2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 - Honolulu, HI, United States
Duration: Apr 15 2007Apr 20 2007

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
ISSN (Print)1520-6149

Other

Other2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07
CountryUnited States
CityHonolulu, HI
Period4/15/074/20/07

Keywords

  • Signal representations
  • Wavelet transforms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

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  • Cite this

    Atkinson, I., & Kamalabadi, F. (2007). Basis selection for wavelet processing of sparse source signals. In 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07 [4217996] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 3). https://doi.org/10.1109/ICASSP.2007.367123