TY - GEN

T1 - Sparse signal representations using the tunable Q-factor wavelet transform

AU - Selesnick, Ivan W.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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.

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.

KW - constant Q transform

KW - sparse signal representation

KW - wavelet transform

UR - http://www.scopus.com/inward/record.url?scp=80055046623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80055046623&partnerID=8YFLogxK

U2 - 10.1117/12.894280

DO - 10.1117/12.894280

M3 - Conference contribution

AN - SCOPUS:80055046623

SN - 9780819487483

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Wavelets and Sparsity XIV

T2 - Wavelets and Sparsity XIV

Y2 - 21 August 2011 through 24 August 2011

ER -