Abstract
Most of the noise models in signal processing are either additive or multiplicative. However, the widely held wavelet shrinkage estimators for signal denoising deal only with additive noise. In this thesis, a new Bayesian wavelet shrinkage model is presented 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 on analysis of Box & Cox transformations in the linear model. In addition, mixture priors governing the transformation are shown useful in predicting the noise from a choice of models. Experimental results are also reported.
Ray, Shubhankar (2002). Bayesian wavelet shrinkage in transformation based linear models. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -2002 -THESIS -R396.