Analysis of multiresolution image denoising schemes using generalized-Gaussian priors

We investigate various connections between wavelet shrinkage methods in image processing and Bayesian estimation using generalized-Gaussian priors. We present fundamental properties of the shrinkage rules implied by the generalized-Gaussian and other heavy-tailed priors. This allows us to show a simple relationship between differentiability of the log prior at zero and the sparsity of the estimates, as well as an equivalence between universal thresholding schemes and Bayesian estimation using a certain generalized-Gaussian prior.