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Optimum Bayes estimator for General Gaussian Distributed (GGD) data inwavelet is provided. The GGD distribution describes a wide class of signalsincluding natural images. A wavelet thresholding method for image denoising isproposed. Interestingly, we show that the Bayes estimator for this class ofsignals is well estimated by a thresholding approach. This result analyticallyconfirms the importance of thresholding for noisy GGD signals. We provide theoptimum soft thresholding value that mimics the behavior of the Bayes estimatorand minimizes the resulting error.  The value of the threshold in BayesShrink, which is one of the most used andefficient soft thresholding methods, has been provided heuristically in theliterature. Our proposed method, denoted by Rigorous BayesShrink(R-BayesShrink), explains the theory of BayesShrink threshold and proves itsoptimality for a subclass of GDD signals. R-BayesShrink improves andgeneralizes the existing BayesShrink for the class of GGD signals. While theBayesShrink threshold is independent from the wavelet coefficient distributionand is just a function of noise and noiseless signal variance, our methodadapts to the distribution of wavelet coefficients of each scale. It is shownthat BayesShrink is a special case of our method when shape parameter in GGD isone or signal follows Laplace distribution. Our simulation results confirm theoptimality of R-BayesShrink in GGD denoising with regards to Peak Signal toNoise Ratio (PSNR) and Structural Similarity (SSIM) index.

Adaptive Bayesian Denoising for General Gaussian Distributed (GGD) Signals in Wavelet Domain