The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods. Most schemes use arbitrary thresholding nonlinearities with ad hoc parameters, or employ computationally expensive adaptive procedures. We overcome these de ciencies with a new wavelet-based denoising technique derived from a simple empirical Bayes approach ba...

We study a Bayesian wavelet shrinkage approach for natural images based on a probability that a given coefficient contains a significant noise-free component, which we call “signal of interest”. First we develop new subband adaptive wavelet shrinkage method of this kind for the generalized Laplacian prior for noise free coefficients. We compare the new shrinkage approach with other subband adap...

Recent research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near{ideal estimation performance in various asymptotic frameworks. However, image processing practice has shown that universal thresholding methods are outperformed by simple Bayesian estimators assuming independent wavelet coeecients and heavy{tailed priors such as Generalized Gaussian distrib...

The normal Bayesian linear model is extended by assigning a flat prior to the δ power of the variance components of the regression coefficients (0<δ≤1⁄2) in order to improve prediction accuracy. In the case of orthonormal regressors, easy-to-compute analytic expressions are derived for the posterior distribution of the shrinkage and regression coefficients. The expected shrinkage is a sigmoid f...

In recent years, wavelet shrinkage has become a very appealing method for data denoising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that i...

Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate distributions are proposed, and correspond...

Wavelet shrinkage and thresholding methods constitute a powerful way to carry out signal denoising, especially when the underlying signal has a sparse wavelet representation. They are computationally fast, and automatically adapt to the smoothness of the signal to be estimated. Nearly minimax properties for simple threshold estimators over a large class of function spaces and for a wide range o...

We develop three novel wavelet domain denoising methods for subband-adaptive, spatiallyadaptive and multivalued image denoising. The core of our approach is estimation of the probability that a given coefficient contains a significant noise-free component, which we call “signal of interest”. In this respect we analyze cases where the probability of signal presence is (i) fixed per subband, (ii)...

The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods. However, most of these methods have free parameters which have to be adjusted or estimated. In this paper, we propose a wavelet-based denoising technique without any free parameters; it is, in this sense, a "universal" method. Our approach uses empirical Bayes...