Adaptive Bayesian Denoising for General Gaussian Distributed Signals

We study behavior of the Bayesian estimator for noisy General Gaussian Distributed (GGD) data and show that this estimator can be well estimated with a simple shrinkage function. The four parameters of this shrinkage function are functions of GGD's shape parameter and data variance. The Shrinkage map, denoted by Rigorous BayesShrink (R-BayesShrink), models the Bayesian estimator for any value of shape parameter. In addition, when the shape parameter is between 0.5 and 1, this Shrinkage function transforms into a simple soft threshold. This result places the role of soft thresholding image denoising methods, such as BayesSkrink, in a new theoretical perspective. Moreover, BayesShrink is shown to be a special case of R-BayesShrink when the shape parameter is one (Laplacian distribution). Our simulation results confirm optimality of R-BayesShrink in GGD signal denoising in the sense of Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) index for a range of shape parameters.