  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.
