Image denoising using scale mixtures of Gaussians in the wavelet domain

J Portilla, V Strela, M J Wainwright and E P Simoncelli

Published in IEEE Trans. Image Processing, vol.12(11), pp. 1338--1351, Nov 2003.
© IEEE Signal Processing Society

Recipient, IEEE Signal Processing Society Best Paper Award, 2008.

DOI: 10.1109/TIP.2003.818640

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  • Description, software & test images
    • 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.
  • Superseded Publications: Strela00a
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  • Image modeling and denoising with random fields of GSMs: Lyu08
  • Image restoration using GSMs: Portilla03a
  • Original technical report version (Sep 2002): Portilla02a
  • Initial conference publication of denoising using GSMs: Portilla01a
  • Initial publication of GSMs as a model for images: Wainwright99b
  • Earlier publication on contextual denoising using local variance prediction: Simoncelli98e
  • Smooth shrinkage as Bayesian least squares estimation: Simoncelli96c
  • Listing of all publications