# Bayesian Wavelet Shrinkage with Beta Priors

## TL;DR

This paper introduces a Bayesian wavelet shrinkage method using Beta priors that incorporate bounded coefficient information, leading to improved performance in noisy signal estimation.

## Contribution

It proposes a novel Bayesian approach with Beta priors for bounded wavelet coefficients, enhancing shrinkage accuracy in non-parametric regression.

## Key findings

- Significant performance improvement over standard methods in low SNR scenarios
- Hyperparameters linked to shrinkage level for easier interpretation
- Effective handling of bounded wavelet coefficients in noisy environments

## Abstract

In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this, we present a Bayesian approach for shrinkage of bounded wavelet coefficients in the context of non-parametric regression. We propose the use of a zero-contaminated beta distribution with a support symmetric around zero as the prior distribution for the location parameter in the wavelet domain in models with additive gaussian errors. The hyperparameters of the proposed model are closely related to the shrinkage level, which facilitates their elicitation and interpretation. For signals with a low signal-to-noise ratio, the associated Bayesian shrinkage rules provide significant improvement in performance in simulation studies when compared with standard techniques.