Im my talk I will consider the problem of representing a function in a non-adaptive fashion such that oscillatory behavior (singularities, shocks, edges, ...) can be handled effectively. In one dimension the wavelet transform does a good job at this task. But as the dimension becomes larger, the wavelet transform does not possess sufficient frequency resolution to describe the subtle geometric phenomena that occur at microscopic scales. <br/><br/>At least on the theoretical side, and for bivariate functions, a satisfactory solution to this problem has been given by the introduction of the curvelet transform by Candes/Donoho and later the shearlet transform by Labate et. al (the latter possessing certain computational advantages). However, all of the known curvelet- and shearlet constructions up to date are rather specific and not localized in space.<br/><br/>I will discuss some more general constructions of shearlets which can be localized in space while still retaining the desirable theoretical properties of previous constructions Show more
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Organisational unit03435 - Schwab, Christoph / Schwab, Christoph
NotesLecture on 2 March 2010.
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