Statistical Modeling of Images with Fields of Gaussian Scale Mixtures

Siwei Lyu and Eero P Simoncelli

Presented at:
Neural Information Processing Systems (NIPS*06),
Vancouver BC, 4-7 Dec 2006.

Published as:
Advances in Neural Information Processing Systems
eds. B. Schölkopf, J Platt and T Hofmann, vol. 19, May 2007.
© MIT Press, Cambridge, MA.

Related publications:
  • Initial description of Gaussian scale mixtures for image modeling: nips-99.
  • Local Gaussian scale mixture model, with denoising: IEEE TIP 12(11), 2003.
  • Nonlinear (divisive) multi-scale decomposition based on random field model: spie-07.


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.
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