Wavelets and related multiresolution ideas are playing with a very
limited vocabulary; that is, with roughly isotropic elements occurring
at all scales and locations. Hence, they are not especially
well-suited for extracting or representing the image geometry.
This talk will introduce newly developed multiscale systems like
curvelets and ridgelets which are very different form wavelet-like
systems. In particular they have very distinct geometric features.
Curvelets and ridgelets take the the form of basis elements which
exhibit very high directional sensitivity and are highly anisotropic.
In two-dimensions, they are localized along curves, in three
dimensions along sheets, etc. In two dimensions for instance,
curvelets are in some sense provably optimal for representing or
extracting information along curved singularities. This is unlike
any other system in current use.
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