Image denoising using scale mixtures of Gaussians in the wavelet domain

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

Research output: Contribution to journalArticle

Abstract

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
Volume12
Issue number11
DOIs
StatePublished - Nov 2003

Fingerprint

Scale Mixture
Image denoising
Image Denoising
Random variables
Wavelets
Coefficient
Multiplier
Least Squares Estimate
Weighted Average
Gaussian White Noise
Independent Random Variables
Digital Image
Mean Squared Error
Statistical Model
Adjacent
Statistical Models
Scalar
Estimate
Demonstrate
Simulation

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Image denoising using scale mixtures of Gaussians in the wavelet domain. / Portilla, Javier; Strela, Vasily; Wainwright, Martin J.; Simoncelli, Eero.

In: IEEE Transactions on Image Processing, Vol. 12, No. 11, 11.2003, p. 1338-1351.

Research output: Contribution to journalArticle

Portilla, Javier ; Strela, Vasily ; Wainwright, Martin J. ; Simoncelli, Eero. / Image denoising using scale mixtures of Gaussians in the wavelet domain. In: IEEE Transactions on Image Processing. 2003 ; Vol. 12, No. 11. pp. 1338-1351.
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