Locally Adaptive Probabilistic Wavelet Shrinkage Algorithms and Application to Colour 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". We develop three novel wavelet domain denoising methods for subband-adaptive, spatially adaptive and multivalued image denoising. In this respect we analyze cases where the probability of signal presence is (i) fixed per sub band, (ii) conditioned on a local spatial context and (iii) conditioned on information from multiple image bands . All the probabilities are estimated assuming generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms in terms of mean squared error Bayesian thresholding approaches. Spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and of higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.