Image restoration using Gaussian scale mixtures in the wavelet domain

A statistical model for images decomposed in an overcomplete wavelet pyramid is described. Each neighborhood of pyramid coefficients is modeled as the product of a Gaussian vector of known covariance, and an independent hidden positive scalar random variable. We propose an efficient Bayesian estimator for the pyramid coefficients of an image degraded by linear distortion (e.g., blur) and additive Gaussian noise. We demonstrate the quality of our results in simulations over a wide range of blur and noise levels.