Statistical modeling of images with fields of Gaussian scale mixtures

S Lyu and E P Simoncelli

Published in Adv. Neural Information Processing Systems (NIPS*06), 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This paper has been superseded by: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
S Lyu and E P Simoncelli.
IEEE Trans. Pattern Analysis and Machine Intelligence, vol.31(4), pp. 693--706, Apr 2009.


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    • 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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  • Initial description of Gaussian scale mixtures for image modeling: Wainwright99b
  • Local Gaussian scale mixture model, with denoising: Portilla03
  • Nonlinear (divisive) multi-scale decomposition based on random field model: Lyu07a
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