Philipp Grohs
Definability and stability of multiscale decompositions for manifold-valued data.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Philipp Grohs, Johannes Wallner
Subjects: Differential Geometry
AbstractWe discuss multiscale representations of discrete manifold-valued data. As it
turns out that we cannot expect general manifold-analogues of biorthogonal
wavelets to possess perfect reconstruction, we focus our attention on those
constructions which are based on upscaling operators which are either
interpolating or midpoint-interpolating. For definable multiscale
decompositions we obtain a stability result.Continuous Shearlet Tight Frames.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Philipp Grohs
Subjects: Functional Analysis
AbstractBased on the shearlet transform we present a general construction of
continuous tight frames for $L^2(\mathbb{R}^2)$ from any sufficiently smooth
function with anisotropic moments. This includes for example compactly
supported systems, piecewise polynomial systems, or both. From our earlier
results it follows that these systems enjoy the same desirable approximation
properties for directional data as the previous bandlimited and very specific
constructions due to Kutyniok and Labate.Continuous Shearlet Frames and Resolution of the Wavefront Set.
Tue, 09/22/2009 - 14:09 — SomNambulAuthors: Philipp Grohs
Subjects: Functional Analysis
AbstractIn recent years directional multiscale transformations like the curvelet- or
shearlet transformation have gained considerable attention. The reason for this
is that these transforms are, unlike more traditional transforms like wavelets,
able to efficiently handle data with features along edges. The main result
confirming this property for shearlets is contained in [G. Kutyniok, D. Labate.
Resolution of the Wavefront Set using continuous Shearlets, Trans.
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