Image denoising using scale mixtures of Gaussians in the wavelet domain

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

Research output: Contribution to journalArticlepeer-review


We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an over-complete multiscale 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 estimates 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.

Original languageEnglish (US)
Pages (from-to)1338-1351
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number11
StatePublished - Nov 2003


  • Bayesian estimation
  • Gaussian scale mixtures
  • Hidden Markov model
  • Natural images
  • Noise removal
  • Overcomplete representations
  • Statistical models
  • Steerable pyramid

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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