@article{MaassSagivStarketal.2014, author = {Maaß, Peter and Sagiv, Chen and Stark, Hans-Georg and Torresani, Bruno}, title = {Signal representation, uncertainty principles and localization measures}, series = {Advances in computational mathematics}, volume = {40}, journal = {Advances in computational mathematics}, number = {3}, doi = {10.1007/s10444-014-9341-8}, pages = {597 -- 607}, year = {2014}, subject = {Signalverarbeitung}, language = {en} } @article{LevieStarkLiebetal.2013, author = {Levie, Ron and Stark, Hans-Georg and Lieb, Florian and Sochen, Nir}, title = {Adjoint translation, adjoint observable and uncertainty principles}, series = {Advances in computational mathematics}, volume = {40}, journal = {Advances in computational mathematics}, number = {3}, doi = {10.1007\%2Fs10444-013-9336-x}, pages = {609 -- 627}, year = {2013}, subject = {Signalverarbeitung}, language = {en} } @article{StarkLiebLantzberg2013, author = {Stark, Hans-Georg and Lieb, Florian and Lantzberg, Daniel}, title = {Variance Based Uncertainty Principles and Minimum Uncertainty Samplings}, series = {Applied Mathematics Letters}, volume = {26(2013)}, journal = {Applied Mathematics Letters}, number = {2}, doi = {10.1016/j.aml.2012.08.009}, pages = {189 -- 193}, year = {2013}, subject = {Wavelet}, language = {en} } @inproceedings{LantzbergLiebStarketal.2012, author = {Lantzberg, Daniel and Lieb, Florian and Stark, Hans-Georg and Levie, Ron and Sochen, Nir}, title = {Uncertainty Principles, Minimum Uncertainty Samplings and Translations}, series = {Proceedings of the 20th European Signal Processing Conference (EUSIPCO) 2012, EURASIP}, booktitle = {Proceedings of the 20th European Signal Processing Conference (EUSIPCO) 2012, EURASIP}, isbn = {978-1-4673-1068-0}, issn = {2219-5491}, pages = {799 -- 803}, year = {2012}, subject = {Signalverarbeitung}, language = {en} } @article{StarkSochen2010, author = {Stark, Hans-Georg and Sochen, Nir}, title = {Square integrable group representations and the uncertainty principle}, series = {Journal of Fourier Analysis and Applications}, volume = {17}, journal = {Journal of Fourier Analysis and Applications}, number = {5}, publisher = {Springer}, doi = {10.1007/s00041-010-9157-y}, pages = {916 -- 931}, year = {2010}, subject = {Unsch{\"a}rferelation}, language = {en} } @article{DahlkeKutyniokMaassetal.2008, author = {Dahlke, Stephan and Kutyniok, Gitta and Maaß, Peter and Sagiv, Chen and Stark, Hans-Georg and Teschke, Gerd}, title = {The Uncertainty Principle Associated with the Continuous Shearlet Transform}, series = {International Journal of Wavelets, Multiresolution and Information Processing}, volume = {6}, journal = {International Journal of Wavelets, Multiresolution and Information Processing}, number = {2}, doi = {10.1142/S021969130800229X}, pages = {157 -- 181}, year = {2008}, subject = {Wavelet}, language = {en} } @book{Stark2007, author = {Stark, Hans-Georg}, title = {Wavelets and Signal Processing: An Application-Based Introduction}, publisher = {Technosphera Publishers}, address = {Moskau}, isbn = {978-3642062469}, pages = {150}, year = {2007}, subject = {Wavelet}, language = {en} } @article{StarkRauhutRedenbachetal.2006, author = {Stark, Hans-Georg and Rauhut, Markus and Redenbach, Thomas and R{\"o}sch, Ronald}, title = {Entwicklung eines Systems zur Oberfl{\"a}cheninspektion von Mineralfaserplatten: Ein Beispiel f{\"u}r erfolgreichen Ideentransfer aus der Forschung in die Praxis}, series = {elektrotechnik - Sonderheft Automation Valley}, journal = {elektrotechnik - Sonderheft Automation Valley}, number = {604}, pages = {20 -- 22}, year = {2006}, subject = {Mineralfaser}, language = {de} } @inproceedings{BruhmFischerStark2004, author = {Bruhm, Hartmut and Fischer, Peter and Stark, Hans-Georg}, title = {Optimierung der dynamischen Bahntreue eines Industrieroboters durch datenbankgest{\"u}tzten Reglerentwurf}, series = {Robotik 2004, VDI-Bericht 1841}, volume = {2004}, booktitle = {Robotik 2004, VDI-Bericht 1841}, publisher = {VDI Verlag}, pages = {511 -- 518}, year = {2004}, subject = {Industrieroboter}, language = {de} } @article{LiebStark2018, author = {Lieb, Florian and Stark, Hans-Georg}, title = {Audio inpainting: Evaluation of time-frequency representations and structured sparsity approaches}, series = {Signal Processing}, volume = {2018}, journal = {Signal Processing}, number = {153}, pages = {291 -- 299}, year = {2018}, abstract = {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.}, subject = {Zeit-Frequenz-Darstellung}, language = {en} } @article{LiebBoskampStark2020, author = {Lieb, Florian and Boskamp, Tobias and Stark, Hans-Georg}, title = {Peak detection for MALDI mass spectrometry imaging data using sparse frame multipliers}, series = {Journal of Proteomics}, volume = {2020}, journal = {Journal of Proteomics}, number = {225}, doi = {https://doi.org/10.1016/j.jprot.2020.103852}, pages = {103852 -- 103860}, year = {2020}, abstract = {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.}, subject = {MALDI-MS}, language = {en} } @article{DobrovolskijStark2024, author = {Dobrovolskij, Dascha and Stark, Hans-Georg}, title = {Synthetic demand data generation for individual electricity consumers: Inpainting}, series = {Energy and AI}, volume = {15}, journal = {Energy and AI}, number = {Januar 2024}, pages = {100312 -- 100320}, year = {2024}, abstract = {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.}, subject = {Energieverbrauch}, language = {en} } @article{LiebStarkThielemann2017, author = {Lieb, Florian and Stark, Hans-Georg and Thielemann, Christiane}, title = {A stationary wavelet transform and a time-frequency based spike detection algorithm for extracellular recorded data}, series = {Journal of Neural Engineering}, volume = {2017}, journal = {Journal of Neural Engineering}, number = {14}, doi = {10.1088/1741-2552/aa654b}, pages = {1 -- 13}, year = {2017}, abstract = {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.}, subject = {Neuronales Netz}, language = {en} }