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 - CHAP A1 - Lieb, Florian T1 - Audio Inpainting Using M-Frames T2 - Current Trends in Analysis and Its Applications N2 - Classical short-time Fourier constructions lead to a signal decomposition with a fixed time-frequency resolution. However, having signals with varying features, such time-frequency decompositions are very restrictive. A more flexible and adaptive sampling of the time-frequency plane is achieved by the nonstationary Gabor transform. Here, the resolution can evolve over time or frequency, respectively, by using different windows for the different sampling positions in the time or frequency domain (Multiwindow-frames). This adaptivity in the time-frequency plane leads to a sparser signal representation. In terms of audio inpainting, i.e., filling in blanks of a depleted audio signal, sparsity in some representation space profoundly influences the quality of the reconstructed signal. We will compare this quality using different nonstationary Gabor transforms and the regular Gabor transform with different types of audio signals. KW - Audio inpainting KW - Convex optimization KW - Nonstationary Gabor frames KW - ERBlet Transform KW - Constant-Q transform KW - Mathematik KW - Aufsatzsammlung Y1 - 2013 SN - 978-3-319-12576-3 U6 - https://doi.org/10.1007/978-3-319-12577-0_77 VL - 2015 SP - 705 EP - 713 PB - Springer International Publishing ER - TY - JOUR A1 - Mayer, Margot A1 - Arrizabalaga, Onetsine A1 - Lieb, Florian A1 - Ciba, Manuel A1 - Ritter, Sylvia A1 - Thielemann, Christiane T1 - Electrophysiological investigation of human embryonic stem cell derived neurospheres using a novel spike detection algorithm JF - Biosensors and Bioelectronics N2 - Microelectrode array (MEA) technology in combination with three-dimensional (3D) neuronal cell models derived from human embryonic stem cells (hESC) provide an excellent tool for neurotoxicity screening. Yet, there are significant challenges in terms of data processing and analysis, since neuronal signals have very small amplitudes and the 3D structure enhances the level of background noise. Thus, neuronal signal analysis requires the application of highly sophisticated algorithms. In this study, we present a new approach optimized for the detection of spikes recorded from 3D neurospheres (NS) with a very low signal-to-noise ratio. This was achieved by extending simple threshold-based spike detection utilizing a highly sensitive algorithm named SWTTEO. This analysis procedure was applied to data obtained from hESC-derived NS grown on MEA chips. Specifically, we examined changes in the activity pattern occurring within the first ten days of electrical activity. We further analyzed the response of NS to the GABA receptor antagonist bicuculline. With this new algorithm method we obtained more reliable results compared to the simple threshold-based spike detection. KW - Microelectrode array KW - Neurosphere KW - Spike detection algorithm KW - Human embryonic stem cell-derived neurons KW - SWTTEO KW - Embryonale Stammzelle Y1 - 2018 U6 - https://doi.org/10.1016/j.bios.2017.09.034 VL - 2018 IS - 100 SP - 462 EP - 468 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 - 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 - TY - THES A1 - Lieb, Florian T1 - The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing KW - Signalverarbeitung KW - Wavelet Y1 - 2018 UR - https://elib.suub.uni-bremen.de/peid=D00106720 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 - Mayer, Margot A1 - Thielemann, Christiane A1 - Ciba, Manuel A1 - Lieb, Florian A1 - Ritter, Sylvia T1 - Electrophysiological investigation of human embryonic stem cell derived neurospheres using a novel spike detection algorithm JF - Biosensors and Bioelectronics KW - Microelectrode array KW - Microelectrode arrayNeurosphereSpHuman embryonic stem cell-derived neurons KW - Embryonale Stammzelle Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1016/j.bios.2017.09.034 VL - 2018 IS - 100 SP - 462 EP - 468 ER - TY - JOUR A1 - Lieb, Florian A1 - Knopp, Tobias T1 - A wavelet-based sparse row-action method for image reconstruction in magnetic particle imaging JF - Medical Physics N2 - Purpose Magnetic particle imaging (MPI) is a preclinical imaging technique capable of visualizing the spatio-temporal distribution of magnetic nanoparticles. The image reconstruction of this fast and dynamic process relies on efficiently solving an ill-posed inverse problem. Current approaches to reconstruct the tracer concentration from its measurements are either adapted to image characteristics of MPI but suffer from higher computational complexity and slower convergence or are fast but lack in the image quality of the reconstructed images. Methods In this work we propose a novel MPI reconstruction method to combine the advantages of both approaches into a single algorithm. The underlying sparsity prior is based on an undecimated wavelet transform and is integrated into a fast row-action framework to solve the corresponding MPI minimization problem. Results Its performance is numerically evaluated against a classical FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) approach on simulated and real MPI data. The experimental results show that the proposed method increases image quality with significantly reduced computation times. Conclusions In comparison to state-of-the-art MPI reconstruction methods, our approach shows better reconstruction results and at the same time accelerates the convergence rate of the underlying row-action algorithm. KW - Wavelet KW - Bildgebendes Verfahren KW - Magnetpartikelbildgebung Y1 - 2021 UR - https://doi.org/10.1002/mp.14938 VL - 48 IS - 7 SP - 3893 EP - 3903 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 -