Random Cascades of Gaussian Scale Mixtures for Natural Images
Martin Wainwright,
Eero P Simoncelli,
and
Alan Willsky
To appear in:
Proc 7th IEEE Int'l Conf on Image Processing
Vancouver, 10-13 September 2000.
doi: 10.1109/ICIP.2000.900944
© IEEE Computer Society.
The detail coefficients of orthonormal wavelets applied to natural
images are approximately uncorrelated. Despite this, they are by no
means independent, but exhibit a strong self-reinforcing
characteristic in that if one wavelet coefficient is large in absolute
value, then "nearby" coefficients (where nearness is measured in
scale, position, or orientation) also are more likely to be large in
absolute value. We have developed a class of non-Gaussian multiscale
processes, defined by random coarse-to-fine cascades on trees of
multiresolution coefficients, that exhibit precisely these types of
behavior. These cascades reproduce a rich semi-parametric class of
random variables known as Gaussian scale mixtures (GSM). We
demonstrate that this model class not only captures natural image
statistics, but also facilitates efficient and optimal processing,
which we illustrate by application to image denoising.
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