PhD Defense - Kenneth Niemann Rasmussen
- Fredag 29. juni 2012 kl. 13:00 - 16:00
Kenneth Niemann Rasmussen, Department of Mathematical Sciences, will defend his PhD Thesis "On the construction of flexible frames and bases for decomposition spaces".
ABSTRACT: Wavelets have proven a very useful tool for representing images and sound signals, but new generalized wavelet systems perform even better in certain cases. I have focused on the construction of flexible generalized wavelet systems with a prescribed nature such as compact support.
The constructions are done by using a perturbation principle which allows flexible frames and bases to be constructed from already known frames and bases. These new frames and bases consist of finite linear combinations of shifts and dilates of a single function with sufficient smoothness and decay.
With this principle I have constructed a compactly supported atomic decomposition for Triebel-Lizorkin type spaces and the associated modulation spaces. These spaces are a broad subclass of decomposition spaces built on structured coverings of the frequency space. Furthermore, I have constructed a compactly supported curvelet type frame with the same sparse representation properties as curvelets for appropriate classes of smooth functions. Curvelets are building blocks which give an essentially optimal sparse representation of functions that are C2 except for discontinuities along piecewise C2-curves.
- Department of Mathematical Sciences
- Fredrik Bajers Vej 7G - room G5-112
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