Bayesian wavelet de-noising with the caravan prior

Shota Gugushvili, Frank Van Der Meulen, Moritz Schauer*, Peter Spreij

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.

Original languageEnglish
Pages (from-to)947-978
Number of pages32
JournalESAIM - Probability and Statistics
Volume23
DOIs
Publication statusPublished - 3 Jan 2020

Keywords

  • Caravan prior
  • Discrete wavelet transform
  • Gamma markov chain
  • Gibbs sampler
  • Regression
  • Wavelet de-noising

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