### Abstract

Shrinkage of the empirical wavelet coefficients is an effective way to de-noise signals possessing sparse wavelet transforms. This article outlines a Bayesian approach to wavelet shrinkage, in which the form of the shrinkage function is induced by a particular choice of prior distributions placed on the wavelet coefficients. Our priors are chosen to be mixtures of two normal distributions, one wide and the other narrow, so as to effectively model the sparseness inherent in the wavelet representations of many signals. This particular choice of prior also allows us to obtain a closed-form expression for the shrinkage function (posterior mean) and for the corresponding uncertainty (posterior variance). This uncertainty information is used in turn to generate uncertainty bands for the full signal reconstruction. An automatic, level-dependent scheme is used to adapt the shrinkage functions to each resolution level of coefficients, although subjective information may be incorporated quite easily.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |

Publisher | IEEE |

Pages | 225-228 |

Number of pages | 4 |

State | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Paris, Fr Duration: Jun 18 1996 → Jun 21 1996 |

### Other

Other | Proceedings of the 1996 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis |
---|---|

City | Paris, Fr |

Period | 6/18/96 → 6/21/96 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis*(pp. 225-228). IEEE.

**Signal de-noising using adaptive Bayesian wavelet shrinkage.** / Chipman, Hugh A.; Kolaczyk, Eric D.; McCulloch, Robert.

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

*Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.*IEEE, pp. 225-228, Proceedings of the 1996 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Paris, Fr, 6/18/96.

}

TY - GEN

T1 - Signal de-noising using adaptive Bayesian wavelet shrinkage

AU - Chipman, Hugh A.

AU - Kolaczyk, Eric D.

AU - McCulloch, Robert

PY - 1996

Y1 - 1996

N2 - Shrinkage of the empirical wavelet coefficients is an effective way to de-noise signals possessing sparse wavelet transforms. This article outlines a Bayesian approach to wavelet shrinkage, in which the form of the shrinkage function is induced by a particular choice of prior distributions placed on the wavelet coefficients. Our priors are chosen to be mixtures of two normal distributions, one wide and the other narrow, so as to effectively model the sparseness inherent in the wavelet representations of many signals. This particular choice of prior also allows us to obtain a closed-form expression for the shrinkage function (posterior mean) and for the corresponding uncertainty (posterior variance). This uncertainty information is used in turn to generate uncertainty bands for the full signal reconstruction. An automatic, level-dependent scheme is used to adapt the shrinkage functions to each resolution level of coefficients, although subjective information may be incorporated quite easily.

AB - Shrinkage of the empirical wavelet coefficients is an effective way to de-noise signals possessing sparse wavelet transforms. This article outlines a Bayesian approach to wavelet shrinkage, in which the form of the shrinkage function is induced by a particular choice of prior distributions placed on the wavelet coefficients. Our priors are chosen to be mixtures of two normal distributions, one wide and the other narrow, so as to effectively model the sparseness inherent in the wavelet representations of many signals. This particular choice of prior also allows us to obtain a closed-form expression for the shrinkage function (posterior mean) and for the corresponding uncertainty (posterior variance). This uncertainty information is used in turn to generate uncertainty bands for the full signal reconstruction. An automatic, level-dependent scheme is used to adapt the shrinkage functions to each resolution level of coefficients, although subjective information may be incorporated quite easily.

UR - http://www.scopus.com/inward/record.url?scp=0029713690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029713690&partnerID=8YFLogxK

M3 - Conference contribution

SP - 225

EP - 228

BT - Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis

PB - IEEE

ER -