Sparse signal representations using the tunable Q-factor wavelet transform

Ivan W. Selesnick

doi:10.1117/12.894280

Sparse signal representations using the tunable Q-factor wavelet transform

Ivan W. Selesnick

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Wavelets and Sparsity XIV
DOIs	https://doi.org/10.1117/12.894280
State	Published - 2011
Event	Wavelets and Sparsity XIV - San Diego, CA, United States Duration: Aug 21 2011 → Aug 24 2011

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	8138
ISSN (Print)	0277-786X

Other

Other	Wavelets and Sparsity XIV
Country/Territory	United States
City	San Diego, CA
Period	8/21/11 → 8/24/11

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

Access to Document

10.1117/12.894280

Cite this

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title = "Sparse signal representations using the tunable Q-factor wavelet transform",

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.",

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AB - 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.

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Sparse signal representations using the tunable Q-factor wavelet transform

Abstract

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Keywords

ASJC Scopus subject areas

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