Survey of image denoising techniques <s> b. Adaptive Thresholds <s> The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a "coring" operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise removal algorithm based on a steerable wavelet pyramid. <s> BIB001 </s> Survey of image denoising techniques <s> b. Adaptive Thresholds <s> Abstract When fitting wavelet based models, shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data. This article outlines a Bayesian approach to shrinkage, obtained by placing priors on the wavelet coefficients. The prior for each coefficient consists of a mixture of two normal distributions with different standard deviations. The simple and intuitive form of prior allows us to propose automatic choices of prior parameters. These parameters are chosen adaptively according to the resolution level of the coefficients, typically shrinking high resolution (frequency) coefficients more heavily. Assuming a good estimate of the background noise level, we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients. The latter may be used to assess uncertainty in the reconstruction. Several examples are used to illustrate the method, and comparisons are made with other shrinkage methods. <s> BIB002
SUREShrink  uses a hybrid of the universal threshold and the SURE [Stein's Unbiased Risk Estimator] threshold and performs better than VISUShrink. BayesShrink BIB001 BIB002 minimizes the Bayes' Risk Estimator function assuming Generalized Gaussian prior and thus yielding data adaptive threshold. BayesShrink outperforms SUREShrink most of the times. Cross Validation  replaces wavelet coefficient with the weighted average of neighborhood coefficients to minimize generalized cross validation (GCV) function providing optimum threshold for every coefficient. The assumption that one can distinguish noise from the signal solely based on coefficient magnitudes is violated when noise levels are higher than signal magnitudes. Under this high noise circumstance, the spatial configuration of neighboring wavelet coefficients can play an important role in noise-signal classifications. Signals tend to form meaningful features (e.g. straight lines, curves), while noisy coefficients often scatter randomly.