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
Volume8138
DOIs
StatePublished - 2011
EventWavelets and Sparsity XIV - San Diego, CA, United States
Duration: Aug 21 2011Aug 24 2011

Other

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

Fingerprint

wavelet analysis
Wavelet transforms
Wavelet Transform
Q factors
Sparsity
Invertible
Wavelets
Parseval Frame
Continuous Wavelet Transform
Oversampling
Discrete Approximation
Discrete wavelet transforms
Inverse problems
Fast Fourier transforms
Fast Algorithm
Redundancy
fast Fourier transformations
redundancy
Tuning
Inverse Problem

Keywords

  • constant Q transform
  • sparse signal representation
  • wavelet transform

ASJC Scopus subject areas

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

Cite this

Sparse signal representations using the tunable Q-factor wavelet transform. / Selesnick, Ivan.

Wavelets and Sparsity XIV. Vol. 8138 2011. 81381U.

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

Selesnick, I 2011, Sparse signal representations using the tunable Q-factor wavelet transform. in Wavelets and Sparsity XIV. vol. 8138, 81381U, Wavelets and Sparsity XIV, San Diego, CA, United States, 8/21/11. https://doi.org/10.1117/12.894280
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