The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing

http://nbn-resolving.de/urn:nbn:de:gbv:46-00106720-18
https://elib.suub.uni-bremen.de/peid=D00106720
urn:nbn:de:gbv:46-00106720-18
Lieb, Florian
2018
Universität Bremen: Informatik/Mathematik
Dissertation
Uncertainty principles, nonstationary Gabor frames, wavelet frames, maldi peak picking, audio inpainting, spike detection
Uncertainty relations play a prominent role in signal processing, stating that a signal can not be simultaneously concentrated in the two related domains of the corresponding phase space. In particular, a new uncertainty principle for the affine group, which is directly related to the wavelet transform has lead to a new minimizing waveform. In this thesis, a frame construction is proposed which leads to approximately tight frames based on this minimizing waveform. Frame properties such as the diagonality of the frame operator as well as lower and upper frame bounds are analyzed. Additionally, three applications of such frame constructions are introduced: inpainting of missing audio data, detection of neuronal spikes in extracellular recorded data and peak detection in MALDI imaging data.
DDC
510
2018.09.11/11:13:47
The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing
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