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.
Mots-clés : Caravan prior, discrete wavelet transform, Gamma markov chain, Gibbs sampler, regression, wavelet de-noising
@article{PS_2019__23__947_0,
author = {Gugushvili, Shota and van der Meulen, Frank and Schauer, Moritz and Spreij, Peter},
title = {Bayesian wavelet de-noising with the caravan prior},
journal = {ESAIM: Probability and Statistics},
pages = {947--978},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2019019},
mrnumber = {4046860},
zbl = {1507.62231},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2019019/}
}
TY - JOUR AU - Gugushvili, Shota AU - van der Meulen, Frank AU - Schauer, Moritz AU - Spreij, Peter TI - Bayesian wavelet de-noising with the caravan prior JO - ESAIM: Probability and Statistics PY - 2019 SP - 947 EP - 978 VL - 23 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2019019/ DO - 10.1051/ps/2019019 LA - en ID - PS_2019__23__947_0 ER -
%0 Journal Article %A Gugushvili, Shota %A van der Meulen, Frank %A Schauer, Moritz %A Spreij, Peter %T Bayesian wavelet de-noising with the caravan prior %J ESAIM: Probability and Statistics %D 2019 %P 947-978 %V 23 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2019019/ %R 10.1051/ps/2019019 %G en %F PS_2019__23__947_0
Gugushvili, Shota; van der Meulen, Frank; Schauer, Moritz; Spreij, Peter. Bayesian wavelet de-noising with the caravan prior. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 947-978. doi : 10.1051/ps/2019019. http://archive.numdam.org/articles/10.1051/ps/2019019/
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