Adaptive bayesian wavelet shrinkage

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

Research output: Contribution to journalArticle

386 Scopus citations

Abstract

When fitting wavelet based models, shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data. This article outlines a Bayesian approach to shrinkage, obtained by placing priors on the wavelet coefficients. The prior for each coefficient consists of a mixture of two normal distributions with different standard deviations. The simple and intuitive form of prior allows us to propose automatic choices of prior parameters. These parameters are chosen adaptively according to the resolution level of the coefficients, typically shrinking high resolution (frequency) coefficients more heavily. Assuming a good estimate of the background noise level, we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients. The latter may be used to assess uncertainty in the reconstruction. Several examples are used to illustrate the method, and comparisons are made with other shrinkage methods.

Original languageEnglish (US)
Pages (from-to)1413-1421
Number of pages9
JournalJournal of the American Statistical Association
Volume92
Issue number440
DOIs
StatePublished - Dec 1 1997
Externally publishedYes

Keywords

  • Bayesian estimation
  • Mixture models
  • Uncertainty bands

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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