3-5 August 2022
Universität Klagenfurt
Europe/Vienna timezone

Signal Processing with Gabor Frames: Variational Problems, Compression, and Noise Removal

4 Aug 2022, 14:30
HS 4 (Universität Klagenfurt)

HS 4

Universität Klagenfurt

Talk Statistics Session B4 Statistics


We present solutions for variational problems, compression and noise removal using gabor frames. For an appropriate window function, a signal $ f \in \mathcal{L}^2(\mathbb{R}^d)$ possesses a non-orthogonal gabor frames expansions in terms of the dual frames with unconditional convergence in $ \mathcal{L}^2(\mathcal(R)^d) $. We derive approximate minimizers of variational problems and compression in modulation spaces. Within the Gaussian white noise model we provide minimax bounds for rates of convergence over modulation spaces using soft-thresholding of the Gabor coefficients. Numerical experiments complement the theoretical results. Furthermore we extend our results onto $\alpha$-modulation spaces, providing a flexible Gabor-wavelet transform of signals.

Primary authors

Pavel Tafo (University Marburg) Prof. Hajo Holzmann (Philipps-Universität Marburg)

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