Statistical modeling of images with fields of Gaussian scale mixtures

S Lyu and E P Simoncelli

Presented at:
Neural Information Processing Systems (NIPS*06)

Published in Adv. Neural Information Processing Systems 19, vol.19 pp. 945--952, May 2007.
© MIT Press, Cambridge, MA

This paper has been superseded by:
Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures
by S Lyu and E P Simoncelli.


Download:

  • Reprint (pdf)
    • The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures (GSMs). Here, we use this local description to construct a global field of Gaussian scale mixtures (FoGSM). Specifically, we model subbands of wavelet coefficients as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for FoGSM is feasible, and that samples drawn from an estimated FoGSM model have marginal and joint statistics similar to wavelet coefficients of photographic images. We develop an algorithm for image denoising based on the FoGSM model, and demonstrate substantial improvements over current state-of-the-art denoising method based on the local GSM model.
    Related:
  • Initial description of Gaussian scale mixtures for image modeling: nips-99Scale Mixtures of Gaussians and the Statistics of Natural Images
    by M J Wainwright and E P Simoncelli
  • Local Gaussian scale mixture model, with denoising: IEEE TIP 12(11), 2003Image denoising using scale mixtures of Gaussians in the wavelet domain
    by J Portilla, V Strela, M J Wainwright, and E P Simoncelli
  • Nonlinear (divisive) multi-scale decomposition based on random field model: spie-07Statistically and perceptually motivated nonlinear image representation
    by S Lyu and E P Simoncelli
  • Online Publications