### 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 |

Volume | 8138 |

DOIs | |

State | Published - 2011 |

Event | Wavelets and Sparsity XIV - San Diego, CA, United States Duration: Aug 21 2011 → Aug 24 2011 |

### Other

Other | Wavelets and Sparsity XIV |
---|---|

Country | United States |

City | San Diego, CA |

Period | 8/21/11 → 8/24/11 |

### Fingerprint

### 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

*Wavelets and Sparsity XIV*(Vol. 8138). [81381U] https://doi.org/10.1117/12.894280

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

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

AU - Selesnick, Ivan

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

VL - 8138

BT - Wavelets and Sparsity XIV

ER -