Adaptive Probabilistic Wavelet Shrinkage for Image Denoising

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 adaptive Bayesian shrinkage rules in terms of mean squared error performance. The results demonstrate that the new method outperforms existing Bayesian thresholding rules for natural images. We also extend the new shrinkage method to a spatially adaptive procedure. In the spatially adaptive version of the method, each coefficient is shrunk according to how probable it is that it presents a signal of interest, based on its value, based on a measurement from the local surrounding and based on the global statistical properties of the coefficients in a given subband. The procedure is fully automatic and fast. The new method yields the results that are among the best state-of-the-art ones and it outperforms much more complex recent related methods.