Signal de-noising using adaptive Bayesian wavelet shrinkage

Hugh A. Chipman, Eric D. Kolaczyk, Robert McCulloch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationProceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
PublisherIEEE
Pages225-228
Number of pages4
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Paris, Fr
Duration: Jun 18 1996Jun 21 1996

Other

OtherProceedings of the 1996 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
CityParis, Fr
Period6/18/966/21/96

Fingerprint

Signal denoising
Signal reconstruction
Normal distribution
Wavelet transforms
Uncertainty

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Chipman, H. A., Kolaczyk, E. D., & McCulloch, R. (1996). Signal de-noising using adaptive Bayesian wavelet shrinkage. In 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.

Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. IEEE, 1996. p. 225-228.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chipman, HA, Kolaczyk, ED & McCulloch, R 1996, Signal de-noising using adaptive Bayesian wavelet shrinkage. in 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.
Chipman HA, Kolaczyk ED, McCulloch R. Signal de-noising using adaptive Bayesian wavelet shrinkage. In Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. IEEE. 1996. p. 225-228
Chipman, Hugh A. ; Kolaczyk, Eric D. ; McCulloch, Robert. / Signal de-noising using adaptive Bayesian wavelet shrinkage. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis. IEEE, 1996. pp. 225-228
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