Title: Image Denoising using a Gaussian Scale Mixture in the Wavelet Domain


Authors: Javier Portilla, Vasily Strela, Martin J. Wainwright, and Eero P. Simoncelli 

We describe a method for removing noise from digital images, based
on a statistical model of the coefficients of an overcomplete
multi-scale oriented basis. Neighborhoods of coefficients at
adjacent positions and scales are modeled as the product of two
independent random variables: a Gaussian vector and a hidden
positive scalar multiplier. The latter modulates the local
variance of the coefficients in the neighborhood, and is thus able
to account for the empirically observed correlation between the
amplitudes of pyramid coefficients. Under this model, the Bayesian
least squares estimate of each coefficient reduces to a weighted
average of the local linear (Wiener) estimate over all possible
values of the hidden multiplier variable. We demonstrate through
simulations with images contaminated by additive Gaussian noise of
known covariance that the performance of this method substantially
surpasses that of previously published methods, both visually and
in terms of mean squared error. In addition, we demonstrate the
performance of the algorithm in removing sensor noise from
high-ISO digital camera images.