The local statistical properties of photographic images, when
represented in a multi-scale basis, have been described using scale
mixtures of Gaussians. Here, we use this local description to
construct a global field of Gaussian scale mixtures (FoGSM) model.
Specifically, we model subbands of wavelet coefficients as a product
of a homogeneous Gaussian Markov random field and a second,
exponentiated, homogeneous Gaussian Markov random field. 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, and demonstrate
significant improvements over current state-of-the-art methods based
on the local GSM model.
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