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Abstract:
The statistics of photographic images, when represented using
multi-scale (wavelet) bases, exhibit two striking non-Gaussian
behaviors. First, the marginal densities of the coefficients have
extended heavy tails. Second, the joint densities exhibit variance
dependencies not captured by second-order models. We examine
properties of the class of Gaussian scale mixtures (GSM), and show
that these densities can accurately characterize both the marginal
and joint distributions of natural image wavelet coefficients. This
class of model suggests a Markov structure, in which wavelet
coefficients are linked by hidden scaling variables corresponding
to local image structure. We derive an estimator for these hidden
variables, and show that a nonlinear "normalization" procedure can
be used to Gaussianize the wavelet coefficients.
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