Adaptive image denoising by rigorous Bayesshrink thresholding

Optimum Bayes estimator for General Gaussian Distributed data is provided. The distribution describes a large 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 behaving very similar to a thresholding approach. This will analytically confirm the importance of thresholding in these scenarios. In particular, when noise variance is less than the the noise-free signal variance, the Bayes estimator behaves similar to a soft thresholding method. We provide the optimum soft thresholding value that mimics the behavior of the Bayes estimator and minimizes the resulting error. The method denoted by Rigorous BayesShrink (R-BayesShrink) outperforms BayesShrink that is the existing most used and efficient soft thresholding method. While BayesShrink threshold is calculated by minimizing the Bayes risk numerically, our approach provides the optimum threshold analytically. Our simulation results show that R-BayesShrink outperforms the BayesShrink in most cases.