A Class of Heavy-tailed Multivariate Non-Gaussian Probability Models for Wavelet Coefficients

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It is well documented that the statistical distribution of wavelet coefficients for natural images is non-Gaussian and that neighboring coefficients are highly dependent. In this paper, we propose a new multivariate non-Gaussian probability model to capture the dependencies among neighboring wavelet coefficients in the same scale. The model can be expressed as K exp(-||w||) where w is an N-element vector of wavelet coefficients and ||w|| is a convex combination of l2 norms over subspaces of RN. This model includes the commonly used independent Laplacian model as a special case but it has many more degrees of freedom. Based on this model, the corresponding non-linear threshold (shrinkage) function for denoising is derived using Bayesian estimation theory. Although this function does not have a closed-form solution, a successive substitution method can be used to numerically compute it.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalProceedings of SPIE - The International Society for Optical Engineering
Issue number1
StatePublished - 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003


  • Denoising
  • Non-Gaussian
  • Statistical model
  • 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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