Image denoising using Gaussian scale mixtures in the wavelet domain

Javier Portilla , Vasily Strela , Martin Wainwright, Eero P Simoncelli

Published in:
Technical Report TR2002-831, September 2002
Computer Science Department,
Courant Institute of Mathematical Sciences
New York University

Revised and shortened version appears in:
Image Denoising using a Scale Mixture of Gaussians in the Wavelet Domain
IEEE Trans Image Processing, November 2003.


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.
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