  Optimum Bayes estimator for General Gaussian Distributed (GGD) data in
wavelet is provided. The GGD distribution describes a wide class of signals
including natural images. A wavelet thresholding method for image denoising is
proposed. Interestingly, we show that the Bayes estimator for this class of
signals is well estimated by a thresholding approach. This result analytically
confirms the importance of thresholding for noisy GGD signals. We provide the
optimum soft thresholding value that mimics the behavior of the Bayes estimator
and minimizes the resulting error.
  The value of the threshold in BayesShrink, which is one of the most used and
efficient soft thresholding methods, has been provided heuristically in the
literature. Our proposed method, denoted by Rigorous BayesShrink
(R-BayesShrink), explains the theory of BayesShrink threshold and proves its
optimality for a subclass of GDD signals. R-BayesShrink improves and
generalizes the existing BayesShrink for the class of GGD signals. While the
BayesShrink threshold is independent from the wavelet coefficient distribution
and is just a function of noise and noiseless signal variance, our method
adapts to the distribution of wavelet coefficients of each scale. It is shown
that BayesShrink is a special case of our method when shape parameter in GGD is
one or signal follows Laplace distribution. Our simulation results confirm the
optimality of R-BayesShrink in GGD denoising with regards to Peak Signal to
Noise Ratio (PSNR) and Structural Similarity (SSIM) index.
