Bayesian wavelet de-noising with the caravan prior
Journal article, 2019

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.

discrete wavelet transform

Gamma markov chain

Caravan prior

wavelet de-noising

Gibbs sampler



Shota Gugushvili

Wageningen University and Research

Frank van der Meulen

Delft University of Technology

Moritz Schauer

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Peter Spreij

University of Amsterdam

Radboud University

ESAIM - Probability and Statistics

1292-8100 (ISSN) 1262-3318 (eISSN)

Vol. 23 947-978

Subject Categories

Bioinformatics (Computational Biology)

Probability Theory and Statistics

Signal Processing



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