Bayesian wavelet de-noising with the caravan prior

TL;DR

This paper introduces a Bayesian wavelet de-noising method that models dependencies between neighboring coefficients using a Markov chain prior, improving estimation accuracy by leveraging clustering patterns in signals.

Contribution

It proposes the caravan prior, a novel Markov chain-based Bayesian model for wavelet coefficients, and demonstrates its effectiveness through comparisons with existing methods.

Findings

Caravan prior outperforms benchmark methods in estimation error.

The approach enhances visual quality of denoised signals.

Method shows robustness on synthetic and real data.

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.