Image denoising using scale mixtures of Gaussians in the wavelet domain

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

Published in:
IEEE Transactions on Image Processing
12(11):1338-1351, November 2003
© IEEE Signal Processing Society.

Related previous publications:
  • Image restoration using Gaussian scale mixtures in the wavelet domain (icip-03)
  • Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain (icip-01)
  • Scale Mixtures of Gaussians and the Statistics of Natural Images (nips-99)
  • Bayesian denoising of visual images in the wavelet domain (Vidakovic-chapter-99)
  • Noise removal via Bayesian wavelet coring (icip-96)


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 coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimate over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
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