### 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) |
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Title of host publication | Wavelets and Sparsity XIV |

DOIs | |

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 |
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Volume | 8138 |

ISSN (Print) | 0277-786X |

### Other

Other | Wavelets and Sparsity XIV |
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Country | 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

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## Cite this

*Wavelets and Sparsity XIV*[81381U] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8138). https://doi.org/10.1117/12.894280