Bayesian wavelet shrinkage in transformation based normal models

Most of the noise models encountered in signal processing are either additive or multiplicative. However, the widely held wavelet shrinkage estimators for signal denoising deal only with additive noise. We propose a Bayesian wavelet shrinkage model that encompasses both types of noise as well as noise that may exist between these two extremes. In applications such as SAR imaging, where multiplicative noise is predominant, statistical models intended for additive noise removal can effect a fair amount of restoration. This leads us to believe that noise in the signal can be considered as somewhere between multiplicative and additive. The new estimator removes noise by better adapting to the noise on hand. This approach is motivated by the work of Pericchi (1981) on the analysis of Box & Cox (1973) transformations in the linear model. In addition, mixture priors governing the transformation are shown to be useful in predicting the noise from a choice of models. Experimental results are also reported.