@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} } @incollection{Lieb2013, author = {Lieb, Florian}, title = {Audio Inpainting Using M-Frames}, series = {Current Trends in Analysis and Its Applications}, volume = {2015}, booktitle = {Current Trends in Analysis and Its Applications}, publisher = {Springer International Publishing}, isbn = {978-3-319-12576-3}, doi = {10.1007/978-3-319-12577-0_77}, pages = {705 -- 713}, year = {2013}, abstract = {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.}, subject = {Mathematik}, language = {en} } @article{MayerArrizabalagaLiebetal.2018, author = {Mayer, Margot and Arrizabalaga, Onetsine and Lieb, Florian and Ciba, Manuel and Ritter, Sylvia and Thielemann, Christiane}, title = {Electrophysiological investigation of human embryonic stem cell derived neurospheres using a novel spike detection algorithm}, series = {Biosensors and Bioelectronics}, volume = {2018}, journal = {Biosensors and Bioelectronics}, number = {100}, doi = {10.1016/j.bios.2017.09.034}, pages = {462 -- 468}, year = {2018}, abstract = {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.}, subject = {Embryonale Stammzelle}, language = {en} } @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{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} } @phdthesis{Lieb2018, author = {Lieb, Florian}, title = {The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing}, school = {Technische Hochschule Aschaffenburg}, year = {2018}, subject = {Signalverarbeitung}, 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{MayerThielemannCibaetal.2018, author = {Mayer, Margot and Thielemann, Christiane and Ciba, Manuel and Lieb, Florian and Ritter, Sylvia}, title = {Electrophysiological investigation of human embryonic stem cell derived neurospheres using a novel spike detection algorithm}, series = {Biosensors and Bioelectronics}, volume = {2018}, journal = {Biosensors and Bioelectronics}, number = {100}, doi = {https://doi.org/10.1016/j.bios.2017.09.034}, pages = {462 -- 468}, year = {2018}, subject = {Embryonale Stammzelle}, language = {en} } @article{LiebKnopp2021, author = {Lieb, Florian and Knopp, Tobias}, title = {A wavelet-based sparse row-action method for image reconstruction in magnetic particle imaging}, series = {Medical Physics}, volume = {48}, journal = {Medical Physics}, number = {7}, pages = {3893 -- 3903}, year = {2021}, abstract = {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.}, subject = {Wavelet}, 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} }