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Abstract:
Classical smoothness spaces (Sobolev, Besov, etc.) have been a staple for classifying
functional regularity. Unfortunately, they are not well suited for measuring
regularity in image processing or nonlinear partial differential equations.
For example, they are typically not invariant regularity classes for time dependent
nonlinear PDEs. Also, it has long been recognized that they do not provide a very
fine classification of images. This talk will introduce ways to measure regularity
via level sets and study the compressibility of these new regularity spaces.
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