TY - JOUR A1 - Maaß, Peter A1 - Sagiv, Chen A1 - Sochen, Nir A1 - Stark, Hans-Georg T1 - Do uncertainty minimizers attain minimal uncertainty? JF - Journal of fourier analysis and applications KW - Quantenmechanik KW - Unschärferelation Y1 - 2010 U6 - https://doi.org/10.1007/s00041-009-9099-4 VL - 16 IS - 3 SP - 448 EP - 469 ER - TY - JOUR A1 - Maaß, Peter A1 - Sagiv, Chen A1 - Stark, Hans-Georg A1 - Torresani, Bruno T1 - Signal representation, uncertainty principles and localization measures JF - Advances in computational mathematics KW - Signalverarbeitung KW - Bildverarbeitung Y1 - 2014 U6 - https://doi.org/10.1007/s10444-014-9341-8 VL - 40 IS - 3 SP - 597 EP - 607 ER - TY - JOUR A1 - Levie, Ron A1 - Stark, Hans-Georg A1 - Lieb, Florian A1 - Sochen, Nir T1 - Adjoint translation, adjoint observable and uncertainty principles JF - Advances in computational mathematics KW - Signalverarbeitung KW - Bildverarbeitung Y1 - 2013 U6 - https://doi.org/10.1007%2Fs10444-013-9336-x VL - 40 IS - 3 SP - 609 EP - 627 ER - TY - JOUR A1 - Stark, Hans-Georg A1 - Lieb, Florian A1 - Lantzberg, Daniel T1 - Variance Based Uncertainty Principles and Minimum Uncertainty Samplings JF - Applied Mathematics Letters KW - Wavelet Y1 - 2013 U6 - https://doi.org/10.1016/j.aml.2012.08.009 VL - 26(2013) IS - 2 SP - 189 EP - 193 ER - TY - CHAP A1 - Lantzberg, Daniel A1 - Lieb, Florian A1 - Stark, Hans-Georg A1 - Levie, Ron A1 - Sochen, Nir T1 - Uncertainty Principles, Minimum Uncertainty Samplings and Translations T2 - Proceedings of the 20th European Signal Processing Conference (EUSIPCO) 2012, EURASIP KW - Signalverarbeitung Y1 - 2012 SN - 978-1-4673-1068-0 SN - 2219-5491 SP - 799 EP - 803 ER - TY - JOUR A1 - Stark, Hans-Georg A1 - Sochen, Nir T1 - Square integrable group representations and the uncertainty principle JF - Journal of Fourier Analysis and Applications KW - Unschärferelation Y1 - 2014 U6 - https://doi.org/10.1007/s00041-010-9157-y VL - 17 IS - 5 SP - 916 EP - 931 PB - Springer ER - TY - JOUR A1 - Dahlke, Stephan A1 - Kutyniok, Gitta A1 - Maaß, Peter A1 - Sagiv, Chen A1 - Stark, Hans-Georg A1 - Teschke, Gerd T1 - The Uncertainty Principle Associated with the Continuous Shearlet Transform JF - International Journal of Wavelets, Multiresolution and Information Processing KW - Wavelet Y1 - 2008 U6 - https://doi.org/10.1142/S021969130800229X VL - 6 IS - 2 SP - 157 EP - 181 ER - TY - BOOK A1 - Stark, Hans-Georg T1 - Wavelets and Signal Processing: An Application-Based Introduction KW - Wavelet KW - Signalverarbeitung Y1 - 2007 SN - 978-3642062469 PB - Technosphera Publishers CY - Moskau ER - TY - JOUR A1 - Stark, Hans-Georg A1 - Rauhut, Markus A1 - Redenbach, Thomas A1 - Rösch, Ronald T1 - Entwicklung eines Systems zur Oberflächeninspektion von Mineralfaserplatten: Ein Beispiel für erfolgreichen Ideentransfer aus der Forschung in die Praxis JF - elektrotechnik - Sonderheft Automation Valley KW - Mineralfaser KW - Oberflächenprüfung Y1 - 2006 IS - 604 SP - 20 EP - 22 ER - TY - CHAP A1 - Bruhm, Hartmut A1 - Fischer, Peter A1 - Stark, Hans-Georg T1 - Optimierung der dynamischen Bahntreue eines Industrieroboters durch datenbankgestützten Reglerentwurf T2 - Robotik 2004, VDI-Bericht 1841 KW - Industrieroboter KW - Reglerentwurf KW - Dynamik KW - Optimierung KW - Industrieroboter KW - Reglerentwurf KW - Dynamik KW - Optimierung KW - Regelungstechnik Y1 - 2004 VL - 2004 SP - 511 EP - 518 PB - VDI Verlag ER - TY - JOUR A1 - Lieb, Florian A1 - Stark, Hans-Georg T1 - Audio inpainting: Evaluation of time-frequency representations and structured sparsity approaches JF - Signal Processing N2 - Audio signals such as music are known to exhibit distinct and sparse time-frequency patterns. In particular, the short-time Fourier/Gabor transform is widely used for sparsely representing audio signals. In this contribution, such sparsity patterns are exploited to reconstruct missing samples. The quality of reconstruction is evaluated for various kinds of proximal splitting algorithms, time-frequency discretizations and sparsity enforcing constraints. Furthermore, given a time-frequency representation, we investigate the performance of synthesis vs. analysis approaches to the reconstruction problem. The equidistant discretization scheme of Gabor transforms is non-adaptive. It is plausible, that more flexible time-frequency representations like wavelets or ERBlets improve reconstruction of missing audio samples. The numerical results presented in this contribution confirm this conjecture and lead to good reconstruction results even for gaps of contiguously missing samples, whose size is notably larger than reported for inpainting experiments carried out previously. KW - Audio inpainting, Structured sparsity, Proximal splitting, Synthesis/analysis, Non-stationary Gabor frames KW - Zeit-Frequenz-Darstellung KW - Tonsignal Y1 - 2018 UR - https://doi.org/10.1016/j.sigpro.2018.07.012 VL - 2018 IS - 153 SP - 291 EP - 299 ER - TY - JOUR A1 - Lieb, Florian A1 - Boskamp, Tobias A1 - Stark, Hans-Georg T1 - Peak detection for MALDI mass spectrometry imaging data using sparse frame multipliers JF - Journal of Proteomics N2 - MALDI mass spectrometry imaging (MALDI MSI) is a spatially resolved analytical tool for biological tissue analysis by measuring mass-to-charge ratios of ionized molecules. With increasing spatial and mass resolution of MALDI MSI data, appropriate data analysis and interpretation is getting more and more challenging. A reliable separation of important peaks from noise (aka peak detection) is a prerequisite for many subsequent processing steps and should be as accurate as possible. We propose a novel peak detection algorithm based on sparse frame multipliers, which can be applied to raw MALDI MSI data without prior preprocessing. The accuracy is evaluated on a simulated data set in comparison with state-of-the-art algorithms. These results also show the proposed method's robustness to baseline and noise effects. In addition, the method is evaluated on real MALDI-TOF data sets, whereby spatial information can be included in the peak picking process. Significance: The field of proteomics, in particular MALDI Imaging, encompasses huge amounts of data. The processing and preprocessing of this data in order to segment or classify spatial structures of certain peptides or isotope patterns can hence be cumbersome and includes several independent processing steps. In this work, we propose a simple peak-picking algorithm to quickly analyze large raw MALDI Imaging data sets, which has a better sensitivity than current state-of-the-art algorithms. Further, it is possible to get an overall overview of the entire data set showing the most significant and spatially localized peptide structures and, hence, contributes all data driven evaluation of MALDI Imaging data. KW - MALDI imaging, Peak picking, Frame multiplier KW - MALDI-MS KW - Massenspektrometrie Y1 - 2020 UR - https://doi.org/10.1016/j.jprot.2020.103852 U6 - https://doi.org/https://doi.org/10.1016/j.jprot.2020.103852 VL - 2020 IS - 225 SP - 103852 EP - 103860 ER - TY - JOUR A1 - Dobrovolskij, Dascha A1 - Stark, Hans-Georg T1 - Synthetic demand data generation for individual electricity consumers: Inpainting JF - Energy and AI N2 - In this contribution we deal with the problem of producing “reasonable” data, when considering recorded energy consumption data, which are at certain sections incomplete and/or erroneous. This task is important, when energy providers employ prediction models for expected energy consumption, which are based on past recorded consumption data, which then of course should be reliable and valid. In a related contribution Yilmaz (2022), GAN-based methods for producing such “artificial data” have been investigated. In this contribution, we describe an alternative and complementary method based on signal inpainting, which has been successfully applied to audio processing Lieb and Stark (2018). After giving a short overview of the theory of proximity-based convex optimization, we describe and adapt an iterative inpainting scheme to our problem. The usefulness of this approach is demonstrated by analyzing real-world-data provided by a German energy supplier. KW - Energieverbrauch KW - Energieversorgungsunternehmen Y1 - 2024 VL - 15 IS - Januar 2024 SP - 100312 EP - 100320 ER - TY - JOUR A1 - Lieb, Florian A1 - Stark, Hans-Georg A1 - Thielemann, Christiane T1 - A stationary wavelet transform and a time-frequency based spike detection algorithm for extracellular recorded data JF - Journal of Neural Engineering N2 - Objective. Spike detection from extracellular recordings is a crucial preprocessing step when analyzing neuronal activity. The decision whether a specific part of the signal is a spike or not is important for any kind of other subsequent preprocessing steps, like spike sorting or burst detection in order to reduce the classification of erroneously identified spikes. Many spike detection algorithms have already been suggested, all working reasonably well whenever the signal-to-noise ratio is large enough. When the noise level is high, however, these algorithms have a poor performance. Approach. In this paper we present two new spike detection algorithms. The first is based on a stationary wavelet energy operator and the second is based on the time-frequency representation of spikes. Both algorithms are more reliable than all of the most commonly used methods. Main results. The performance of the algorithms is confirmed by using simulated data, resembling original data recorded from cortical neurons with multielectrode arrays. In order to demonstrate that the performance of the algorithms is not restricted to only one specific set of data, we also verify the performance using a simulated publicly available data set. We show that both proposed algorithms have the best performance under all tested methods, regardless of the signal-to-noise ratio in both data sets. Significance. This contribution will redound to the benefit of electrophysiological investigations of human cells. Especially the spatial and temporal analysis of neural network communications is improved by using the proposed spike detection algorithms. KW - spike detection KW - wavelet TEO KW - extracellular recording KW - Neuronales Netz Y1 - 2017 U6 - https://doi.org/10.1088/1741-2552/aa654b VL - 2017 IS - 14 SP - 1 EP - 13 ER -