Sparse signal representations using the tunable Q-factor wavelet transform

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

Abstract

The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented using radix-2 FFTs. The TQWT can also be used as an easily-invertible discrete approximation of the continuous wavelet transform.

Original languageEnglish (US)
Title of host publicationWavelets and Sparsity XIV
DOIs
StatePublished - 2011
EventWavelets and Sparsity XIV - San Diego, CA, United States
Duration: Aug 21 2011Aug 24 2011

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8138
ISSN (Print)0277-786X

Other

OtherWavelets and Sparsity XIV
CountryUnited States
CitySan Diego, CA
Period8/21/118/24/11

Keywords

  • constant Q transform
  • sparse signal representation
  • wavelet transform

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Selesnick, I. W. (2011). Sparse signal representations using the tunable Q-factor wavelet transform. In Wavelets and Sparsity XIV [81381U] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8138). https://doi.org/10.1117/12.894280