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Randomised approximation with Frames


A frame is a family of vectors in a Hilbert space, which allows representation of arbitrary elements by (continuous) superposition. Important examples of frames appear in time-frequency analysis, wavelet analysis and sampling theory.

We propose a new class of algorithms based on randomization for approximating elements (usually functions) with frames. The basic idea is to select randomly frame elements and based on this determine an approximation to a given input vector (signal, function).

Applications include signal and image processing, wireless communication and the numerical treatment of operator equations. In the proposed project we intend to investigate properties of the algorithm, in particular its performance, both theoretically and based on tests wit h computer implementations.

Motivated by very promising results already available for a few special cases, we are convinced that the proposed algorithm will perform very efficiently.

The candidate has gained experience on frame theory, time-frequency analysis, wavelet analysis and (abstract) harmonic analysis in several previous research projects, in particular, in his doctoral thesis and his diploma thesis at the Technical University of Munich.

The candidate will investigate the project at the Numerical Harmonic Analysis Group (NuHAG), University of Vienna, whose key scientists are Prof. H.G. Feichtinger and Prof. K. Grochenig (team leader of MC Exc. Grant). NuHAG is a leading research group in the field of frame theory, time-frequency analysis and sampling theory - both for theoretical and numerical aspects.

The NuHAG team with its expertise will provide an ideal and stimulating international research environment for the proposed project allowing the candidate to strengthen his professional skills in many ways towards a European academic career.

Call for proposal

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Dr. Karl Lueger Ring 1