Project

Instantaneous Frequency in Biomedical Applications

Goal: Nonstationary and non-linear signals do not decompose meaningfully into aggregates of constant amplitude and constant frequency sinusoidal components. For such signals, the notion of frequency as we know loses its effectiveness, and we need to account for the time-varying nature of the process. This need has given rise to the idea of instantaneous frequency, which is often of significant practical importance.
Particularly in biological systems and for biomedical applications, the Instantaneous Frequency is a good descriptor of some physical phenomenon. This project discusses the concept of instantaneous frequency, its various definitions, and the correspondence between the mathematical models formulated for representation of Instantaneous Frequency. Application in several biomedical areas are presented

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Project log

Maximiliano Bueno López
added a research item
Epilepsy is a serious chronic neurological disorder and it can be detected by analyzing an Electroencephalogram acquired from non-invasive methods. Different strategies have been used for the identification of frequencies in EEG signals and the detection of an epileptic seizure, and also for the analysis in the time domain. This paper presents a comparative review of three of the most widely used methods for the analysis of EEG signals in the time and frequency domain: Fourier Transform, Wavelet Transform, and Hilbert Huang Transform. The results presented are obtained from real databases of patients diagnosed with epilepsy.
Maximiliano Bueno López
added a research item
This presentation shows some Hilbert Huang Transform applications for instantaneous frequency detection
Olav Bjarte Fosso
added a research item
This paper presents and discusses the challenge of mode mixing when using the Empirical Mode Decomposition (EMD) to identify intrinsic modes from EEG signals used for neural activity reconstruction. The standard version of the EMD poses some challenges when decomposing signals having intermittency and close spectral proximity in their bands. This is known as the Mode Mixing problem in EMD. Several approaches to solve the issue have been proposed in the literature, but no single technique seems to be universally effective in preserving independent modes after the EMD decomposition. This paper exposes the impact of mode mixing in the process of neural activity reconstruction and reports the results of a performance comparison between a well known strategy, the Ensemble EMD (EEMD), and a new strategy proposed by the authors for mitigating the mode mixing problem. The comparative evaluation shows a more accurate neural reconstruction when employing the strategy proposed by the authors, compared to the use of EEMD and its variants for neural activity reconstruction.
Marta Molinas
added a research item
In this work, a novel identification method of relevant Intrinsic Mode Functions, obtained from Electroencephalographic signals, by using an entropy criteria is proposed. The idea is to reduce the number of Intrinsic Mode Functions that are necessary for the electroencephalographic source reconstruction. An entropy cost function is applied on the Intrinsic Mode Functions generated by the Empirical Mode Decomposition for automatic IMF selection. The resulting Enhanced Empirical Mode Decomposition is evaluated in simulated and real data bases containing normal and epileptic activity by means of a relative error measure. The proposed approach shows to improve the electroencephalographic source reconstruction specifically for epileptic seizure detection.
Marta Molinas
added 13 research items
Aim of the project: David against Goliath: Could Small Data from single-channel or low-density EEG compete in the Big Data contest with high density EEG on equal footing or could David and Goliath join forces? Yes, they can and FlexEEG will show how. FlexEEG proposes a new concept of dry single-channel EEG with enriched information extraction that will materialize into a sensor-embedded data-driven approach to the real-time localization of brain activity. Level of impact and excellence: While a laboratory setting and research-grade electroencephalogram (EEG) equipment will ensure a controlled environment and high-quality multiple-channel EEG recording, there are situations and populations for which this is not suitable. FlexEEG aims at validating a new concept of single-channel or low-density EEG system that while being portable and relying on dry-sensor technology, will produce recordings of comparable quality to a research-grade EEG system but will surpass the capabilities and scope of conventional lab-based EEG equipment: In short, a single more intelligent EEG sensor could defeat high-density EEG. Conventional EEG is challenged by high cost, immobility of equipment and the use of inconvenient conductive gels. Ease of use and quality of information extraction are much awaited in a new EEG concept that produces recording of comparable quality to a research-grade system but that puts EEG within the reach of everyone. FlexEEG will bring that. This project will exploit methods of inverse problems, data-driven non-linear and non-stationary signal analysis 1,2,3 combined with dry-sensor technology to develop a pioneering system that will enable a single, properly localized EEG channel, to provide research-grade information comparable to and surpassing the capabilities of high density-channel EEG. Through this, the range of applications of EEG signals will be expanded from clinical diagnosis and research to healthcare, to better understanding of cognitive processes, to learning and education, and to today hidden/unknown properties behind ordinary human activity and ailments (e.g. walking, sleeping, complex cognitive activity, chronic pain, insomnia). This will be made possible by the implementation of adaptive non-linear and non-stationary data analysis tools in combination with inverse modelling to solve the brain-mapping problem.
In this paper, imagined speech classification is performed with an implementation in Python and using scikit-learn library, to create a toolbox intended for real-time classification. To this aim, the Discrete Wavelet Transform with the mother function Biorthogonal 2.2 is used to then compute the instantaneous and Teager energy distribution for feature extraction. Then, random forest is implemented as a classifier with 10-folds cross-validation. The set of experiments consists of imagined speech classification, linguistic activity and inactivity classification and subjects identification. The experiments were performed using a dataset of 27 subjects which imagined 33 repetitions of 5 words in Spanish up, down, left, right and select. The accuracy obtained with the models were 0.77, 0.78 and 0.98 respectively for each task. The high accuracy rates obtained as a result attest for the feasibility of the proposed method for subject identification.
When brain activity is translated into commands for real applications, the potential for human capacities augmentation is promising. In this paper, EMD is used to decompose EEG signals during Imagined Speech in order to use it as a biometric marker for creating a Biometric Recognition System. For each EEG channel, the most relevant Intrinsic Mode Functions (IMFs) are decided based on the Minkowski distance, and for each IMF 4 features are computed: Instantaneous and Teager energy distribution and Higuchi and Petrosian Fractal Dimension. To test the proposed method, a dataset with 20 subjects who imagined 30 repetitions of 5 words in Spanish, is used. Four classifiers are used for this task - random forest, SVM, naive Bayes, and k-NN - and their performances are compared. The accuracy obtained (up to 0.92 using Linear SVM) after 10-folds cross-validation suggest that the proposed method based on EMD can be valuable for creating EEG-based biometrics of imagined speech for Subjects identification.
Maximiliano Bueno López
added a research item
This paper shows a method to locate actives sources from pre-processed electroencephalographic signals. These signals are processed using multivariate empirical mode decomposition (MEMD). The intrinsic mode functions are analyzed through the Hilbert-Huang spectral entropy. A cost function is proposed to automatically select the intrinsic mode functions associated with the lowest spectral entropy values and they are used to reconstruct the neural activity generated by the active sources. Multiple sparse priors are used to locate the active sources with and without multivariate empirical mode decomposition and the performance is estimated using the Wasserstein metric. The results were obtained for conditions with high noise (Signal-to-Noise-Ratio of -5dB), where the estimated location, for five sources, was better for multiple sparse prior with Multivariate Empirical Mode Decomposition, and with low noise (Signal-to-Noise-Ratio of 20dB), where the estimated location, for three sources, was better for multiple sparse prior without MEMD.
Maximiliano Bueno López
added a research item
Empirical Mode Decomposition (EMD) is an adaptive time-frequency analysis method, which is very useful for extracting information from noisy nonlinear or nonstationary data. The applications of this technique to Biomedical Signal analysis has increased and is now common to find publications that use EMD to identify behaviors in the brain or heart. In this work, a novel identification method of relevant IMFs, obtained from EEG signals, using an entropy analysis is proposed. The idea is to reduce the number of IMFs that are necessary for the reconstruction of neural activity. The entropy cost function is applied on the IMFs generated by the EMD. The efficacy of the proposed method has been demonstrated in a simulated and real data base. A relative error measure has been used to validate our proposal.
Marta Molinas
added 4 research items
The Empirical Mode Decomposition (EMD) is a signal analysis method that separates multi-component signals into single oscillatory modes called intrinsic mode functions (IMFs), each of which can generally be associated to a physical meaning of the process from which the signal is obtained. When the phenomena of mode mixing occur, as a result of the EMD sifting process, the IMFs can lose their physical meaning hindering the interpretation of the results of the analysis. In the paper, "One or Two frequencies? The Empirical Mode Decomposition Answers", Gabriel Rilling and Patrick Flandrin [3] presented a rigorous mathematical analysis that explains how EMD behaves in the case of a composite two-tones signal and the amplitude and frequency ratios by which EMD will perform a good separation of tones. However, the authors did not propose a solution for separating the neighboring tones that will naturally remain mixed after an EMD. In this paper, based on the findings by Rilling and Flandrin, a method that can separate neighbouring spectral components, that will naturally remain within a single IMF, is presented. This method is based on reversing the conditions by which mode mixing occurs and that were presented in the map by Rilling and Flandrin in the above mentioned paper. Numerical experiments with signals containing closely spaced spectral components shows the effective separation of modes that EMD can perform after this principle is applied. The results verify also the regimes presented in the theoretical analysis by Rilling and Flandrin.
Nonlinear and/or nonstationary properties have been observed in measurements coming from microgrids in modern power systems and biological systems. Generally, signals from these two domains are analyzed separately although they may share many features and can bene�t from the use of the same methodology. This paper explores the use of Hilbert-Huang transform (HHT) and Wavelet transform (WT) for instantaneous frequency detection in these two di�erent domains, in the search for a new adaptive algorithm that can be used to analyze signals from these domains without the need to make many a-priory adjustments. Two signals are selected for the investigation: a synthetic signal containing a time varying component and a real EEG signal obtained from The Ecole Polytechnique Federale de Lausanne. The two signals are analyzed with HHT and a discrete WT (DWT). When interpreting the results obtained with the synthetic signal, it is clear that the HHT reproduces the true components, while the DWT does not, making a meaningful interpretation of the modes more challenging. The results obtained when applying HHT to the EEG signal shows 5 modes of oscillations that appear to be well behaved Intrinsic Mode Functions (IMFs), while the results with DWT are harder to interpret in terms of modes. The DWT requires a higher level of decomposition to get closer to the results of the HHT, however multi-frequency bands may be useful depending on the application. The reconstruction of the signal from the approximation and detail coe�cients shows a good behavior and this is one application for DWT especially for removing the unwanted noise of a signal.
Continuous biological signals, like blood pressure recordings, exhibit non-linear and non-stationary properties which must be considered when analyzing them. Heart rate variability analyses have identified several frequency components and their autonomic origin. There is need for more knowledge on the time-changing properties of these frequencies. The power spectrum, continuous wavelet transform and Hilbert-Huang transform are applied on a continuous blood pressure signal to investigate how the different methods compare to each other. The Hilbert-Huang transform shows high ability to analyzing such data, and can, by identifying instantaneous frequency shifts, provide new insights into the nature of these kinds of data.
Marta Molinas
added a project goal
Nonstationary and non-linear signals do not decompose meaningfully into aggregates of constant amplitude and constant frequency sinusoidal components. For such signals, the notion of frequency as we know loses its effectiveness, and we need to account for the time-varying nature of the process. This need has given rise to the idea of instantaneous frequency, which is often of significant practical importance.
Particularly in biological systems and for biomedical applications, the Instantaneous Frequency is a good descriptor of some physical phenomenon. This project discusses the concept of instantaneous frequency, its various definitions, and the correspondence between the mathematical models formulated for representation of Instantaneous Frequency. Application in several biomedical areas are presented