Bayesian wavelet-based signal estimation using non-informative priors

The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful signal denoising methods. Most existing schemes involve arbitrary thresholding nonlinearities and ad hoc threshold levels, or computationally expensive signal-adaptive procedures. Furthermore, because the DWT is not a translation-invariant (TI) transform, results of processing depend on the relative alignment between data and wavelets in a complicated manner. In the context of denoising, this non-stationarity can produce undesirable ("pseudo-Gibbs" or "blocking") artifacts. To overcome these deficiencies, we propose a new wavelet-based signal denoising technique derived using the theory of non-informative Bayesian priors. The resulting estimator is TI and employs a very simple fixed non-linear shrinkage/thresholding rule. Remarkably, our new approach is very computationally efficient and performs better than standard methods that are more computationally demanding.