Geometric properties of Gabor frames with a random window
Publication date
2017-09-01
Authors
Salanevich, Palina
Pfander, Götz E.
Editors
Anbarjafari, Gholamreza
Kivinukk, Andi
Tamberg, Gert
Advisors
Supervisors
Document Type
Part of book
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Abstract
In this paper we address various geometric properties of frames, such as spark, coherence, restricted isometry property, and frame order statistics. These properties play crucial role in various signal processing problems, including compressive sensing, phase retrieval, and quantization. We focus on a particular case of structured frames, namely on Gabor frames, where frame vectors are time and frequency shifts of a random window, and show that geometric properties of Gabor frames are close to optimum, which is usually demonstrated by Gaussian frames with independent vectors.
Keywords
Signal Processing, Statistics, Probability and Uncertainty, Analysis, Statistics and Probability, Applied Mathematics
Citation
Salanevich, P & Pfander, G E 2017, Geometric properties of Gabor frames with a random window. in G Anbarjafari, A Kivinukk & G Tamberg (eds), 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017., 8024460, IEEE, pp. 183-187, 12th International Conference on Sampling Theory and Applications, SampTA 2017, Tallinn, Estonia, 3/07/17. https://doi.org/10.1109/SAMPTA.2017.8024460, conference