Image denoising using a local Gaussian scale mixture model in the wavelet domain

Vasily Strela, Javier Portilla, Eero Simoncelli

Research output: Contribution to journalArticlepeer-review


The statistics of photographic images, when decomposed in a multiscale wavelet basis, exhibit striking non-Gaussian behaviors. The joint densities of clusters of wavelet coefficients (corresponding to basis functions at nearby spatial positions, orientations and scales) are well-described as a Gaussian scale mixture: A jointly Gaussian vector multiplied by a hidden scaling variable. We develop a maximum likelihood solution for estimating the hidden variable from an observation of the cluster of coefficients contaminated by additive Gaussian noise. The estimated hidden variable is then used to estimate the original noise-free coefficients. We demonstrate the power of this model through numerical simulations of image denoising.

Original languageEnglish (US)
Pages (from-to)363-371
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
Issue number1
StatePublished - Dec 4 2000


  • Adaptive Wiener filtering
  • Denoising
  • Gaussian scale mixture
  • Multiresolution
  • Natural image statistics
  • Wavelet

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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