Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis

Perceptual Constraints and the Dynamics of Movement Execution and Learning

Guidance by simple visual patterns has been reported to facilitate performance of difficult coordination patterns. This kind of guidance, however, might significantly alter coordination dynamics and learning. Experiment 1 investigated the effect of visual guidance on the organization of bimanual coordination. Anti-phase 1:1 was performed without (i) augmented information, (ii) under metronome pacing, and (iii) under visual guidance by a Lissajous plot. DFA analysis revealed that the temporal dynamics of amplitudes and relative phase values deviated from the typical 1/f variation towards more random variation under visual guidance. Complexity of amplitudes, periods and relative phases, as measured by multiscale entropy, were also lowered in visual guidance. Experiment 2 investigated whether the dynamical effects visual guidance have any role in learning. Specifically, the effects of practicing bimanual coordination at 90° of relative phase with constant visual guidance by a Lissajous plot, a fading schedule of guidance and no guidance were investigated. After practice, individuals were tested in independent execution (with no guidance) and under visual guidance. Practice conditions did not affect temporal correlation of phases, amplitudes of periods at final tests. Complexity of amplitudes and periods showed some increase in the no guidance test for the group that practiced under constant visual guidance, but not for the other groups. A specificity of practice effect on complexity was found: performance in the visually guided test was associated with a general decrease in complexity for all groups (replicating Experiment 1), except for participants that practiced with constant visual guidance

Multivariate time-frequency analysis

Recent advances in time-frequency theory have led to the development of high resolution time-frequency algorithms, such as the empirical mode decomposition (EMD) and the synchrosqueezing transform (SST). These algorithms provide enhanced localization in representing time varying oscillatory components over conventional linear and quadratic time-frequency algorithms. However, with the emergence of low cost multichannel sensor technology, multivariate extensions of time-frequency algorithms are needed in order to exploit the inter-channel dependencies that may arise for multivariate data. Applications of this framework range from filtering to the analysis of oscillatory components. To this end, this thesis first seeks to introduce a multivariate extension of the synchrosqueezing transform, so as to identify a set of oscillations common to the multivariate data. Furthermore, a new framework for multivariate time-frequency representations is developed using the proposed multivariate extension of the SST. The performance of the proposed algorithms are demonstrated on a wide variety of both simulated and real world data sets, such as in phase synchrony spectrograms and multivariate signal denoising. Finally, multivariate extensions of the EMD have been developed that capture the inter-channel dependencies in multivariate data. This is achieved by processing such data directly in higher dimensional spaces where they reside, and by accounting for the power imbalance across multivariate data channels that are recorded from real world sensors, thereby preserving the multivariate structure of the data. These optimized performance of such data driven algorithms when processing multivariate data with power imbalances and inter-channel correlations, and is demonstrated on the real world examples of Doppler radar processing.Open Acces

Multivariate multiscale complexity analysis

Established dynamical complexity analysis measures operate at a single scale and thus fail to quantify inherent long-range correlations in real world data, a key feature of complex systems. They are designed for scalar time series, however, multivariate observations are common in modern real world scenarios and their simultaneous analysis is a prerequisite for the understanding of the underlying signal generating model. To that end, this thesis first introduces a notion of multivariate sample entropy and thus extends the current univariate complexity analysis to the multivariate case. The proposed multivariate multiscale entropy (MMSE) algorithm is shown to be capable of addressing the dynamical complexity of such data directly in the domain where they reside, and at multiple temporal scales, thus making full use of all the available information, both within and across the multiple data channels. Next, the intrinsic multivariate scales of the input data are generated adaptively via the multivariate empirical mode decomposition (MEMD) algorithm. This allows for both generating comparable scales from multiple data channels, and for temporal scales of same length as the length of input signal, thus, removing the critical limitation on input data length in current complexity analysis methods. The resulting MEMD-enhanced MMSE method is also shown to be suitable for non-stationary multivariate data analysis owing to the data-driven nature of MEMD algorithm, as non-stationarity is the biggest obstacle for meaningful complexity analysis. This thesis presents a quantum step forward in this area, by introducing robust and physically meaningful complexity estimates of real-world systems, which are typically multivariate, finite in duration, and of noisy and heterogeneous natures. This also allows us to gain better understanding of the complexity of the underlying multivariate model and more degrees of freedom and rigor in the analysis. Simulations on both synthetic and real world multivariate data sets support the analysis

An Inquiry: Effectiveness of the Complex Empirical Mode Decomposition Method, the Hilbert-Huang Transform, and the Fast-Fourier Transform for Analysis of Dynamic Objects

A review of current signal analysis tools show that new techniques are required for an enhanced fidelity or data integrity. Recently, the Hilbert-Huang transform (HHT) and its inherent property, the Empirical Mode Decomposition (EMD) technique, have been formerly investigated. The technique of Complex EMD (CEMD) was also explored. The scope of this work was to assess the CEMD technique as an innovative analysis tool. Subsequent to this, comparisons between applications of the Hilbert transform (HT) and the Fast-Fourier transform (FFT) were analyzed. MATLAB was implemented to model signal decomposition and the execution of mathematical transforms for generating results. The CEMD technique successfully decomposed the data into its oscillatory modes. After comparative graphical analysis of the HT and FFT, application of the HT provided marginal enhancements of the data modeled previously by the FFT. Altogether, the HHT could not be determined as a helpful analysis tool. Nevertheless, the CEMD technique, an inherent component of the HHT, exhibited a possible improvement as an analysis tool for signal processing data. Further evaluation of the CEMD technique and the HHT is needed for ultimate determination of their usefulness as an analysis tool

A Study of Biomedical Time Series Using Empirical Mode Decomposition : Extracting event-related modes from EEG signals recorded during visual processing of contour stimuli

Noninvasive neuroimaging techniques like functional Magnetic Resonance Imaging (fMRI) and/or Electroencephalography (EEG) allow researchers to investigate and analyze brain activities during visual processing. EEG offers a high temporal resolution at a level of submilliseconds which can be combined favorably with fMRI which has a good spatial resolution on small spatial scales in the millimeter range. These neuroimaging techniques were, and still are instrumental in the diagnoses and treatments of neurological disorders in the clinical applications. In this PhD thesis we concentrate on lectrophysiological signatures within EEG recordings of a combined EEG-fMRI data set which where taken while performing a contour integration task. The estimation of location and distribution of the electrical sources in the brain from surface recordings which are responsible for interesting EEG waves has drawn the attention of many EEG/MEG researchers. However, this process which is called brain source localization is still one of the major problems in EEG. It consists of solving two modeling problems: forward and inverse. In the forward problem, one is interested in predicting the expected potential distribution on the scalp from given electrical sources that represent active neurons in the head. These evaluations are necessary to solve the inverse problem which can be defined as the problem of estimating the brain sources that generated the measured electrical potentials. This thesis presents a data-driven analysis of EEG data recorded during a combined EEG/fMRI study of visual processing during a contour integration task. The analysis is based on an ensemble empirical mode decomposition (EEMD) and discusses characteristic features of event related modes (ERMs) resulting from the decomposition. We identify clear differences in certain ERMs in response to contour vs non-contour Gabor stimuli mainly for response amplitudes peaking around 100 [ms] (called P100) and 200 [ms] (called N200) after stimulus onset, respectively. We observe early P100 and N200 responses at electrodes located in the occipital area of the brain, while late P100 and N200 responses appear at electrodes located in frontal brain areas. Signals at electrodes in central brain areas show bimodal early/late response signatures in certain ERMs. Head topographies clearly localize statistically significant response differences to both stimulus conditions. Our findings provide an independent proof of recent models which suggest that contour integration depends on distributed network activity within the brain. Next and based on the previous analysis, a new approach for source localization of EEG data based on combining ERMs, extracted with EEMD, with inverse models has been presented. As the first step, 64 channel EEG recordings are pooled according to six brain areas and decomposed, by applying an EEMD, into their underlying ERMs. Then, based upon the problem at hand, the most closely related ERM, in terms of frequency and amplitude, is combined with inverse modeling techniques for source localization. More specifically, the standardized low resolution brain electromagnetic tomography (sLORETA) procedure is employed in this work. Accuracy and robustness of the results indicate that this approach deems highly promising in source localization techniques for EEG data. Given the results of analyses above, it can be said that EMD is able to extract intrinsic signal modes, ERMs, which contain decisive information about responses to contour and non-contour stimuli. Hence, we introduce a new toolbox, called EMDLAB, which serves the growing interest of the signal processing community in applying EMD as a decomposition technique. EMDLAB can be used to perform, easily and effectively, four common types of EMD: plain EMD, ensemble EMD (EEMD), weighted sliding EMD (wSEMD) and multivariate EMD (MEMD) on the EEG data. The main goal of EMDLAB toolbox is to extract characteristics of either the EEG signal by intrinsic mode functions (IMFs) or ERMs. Since IMFs reflect characteristics of the original EEG signal, ERMs reflect characteristics of ERPs of the original signal. The new toolbox is provided as a plug-in to the well-known EEGLAB which enables it to exploit the advantageous visualization capabilities of EEGLAB as well as statistical data analysis techniques provided there for extracted IMFs and ERMs of the signal

Advanced bioelectrical signal processing methods: Past, present and future approach - Part III: Other biosignals

Analysis of biomedical signals is a very challenging task involving implementation of various advanced signal processing methods. This area is rapidly developing. This paper is a Part III paper, where the most popular and efficient digital signal processing methods are presented. This paper covers the following bioelectrical signals and their processing methods: electromyography (EMG), electroneurography (ENG), electrogastrography (EGG), electrooculography (EOG), electroretinography (ERG), and electrohysterography (EHG).Web of Science2118art. no. 606

Методе за оцену електричне активности глатких мишића

Recording of the smooth stomach muscles' electrical activity can be performed by means of Electrogastrography (EGG), a non-invasive technique for acquisition that can provide valuable information regarding the functionality of the gut. While this method had been introduced for over nine decades, it still did not reach its full potential. The main reason for this is the lack of standardization that subsequently led to the limited reproducibility and comparability between different investigations. Additionally, variability between many proposed recording approaches could make EGG unappealing for broader application. The aim was to provide an evaluation of a simplified recording protocol that could be obtained by using only one bipolar channel for a relatively short duration (20 minutes) in a static environment with limited subject movements. Insights into the most suitable surface electrode placement for EGG recording was also presented. Subsequently, different processing methods, including Fractional Order Calculus and Video-based approach for the cancelation of motion artifacts – one of the main pitfalls in the EGG technique, was examined. For EGG, it is common to apply long-term protocols in a static environment. Our second goal was to introduce and investigate the opposite approach – short-term recording in a dynamic environment. Research in the field of EGG-based assessment of gut activity in relation to motion sickness symptoms induced by Virtual Reality and Driving Simulation was performed. Furthermore, three novel features for the description of EGG signal (Root Mean Square, Median Frequency, and Crest Factor) were proposed and its applicability for the assessment of gastric response during virtual and simulated experiences was evaluated. In conclusion, in a static environment, the EGG protocol can be simplified, and its duration can be reduced. In contrast, in a dynamic environment, it is possible to acquire a reliable EGG signal with appropriate recommendations stated in this Doctoral dissertation. With the application of novel processing techniques and features, EGG could be a useful tool for the assessment of cybersickness and simulator sickness.Снимање електричне активности глатких мишића желуца може се реализовати употребом електрогастрографије (ЕГГ), неинвазивне методе која пружа значајне информације везане за функционисање органа за варење. Упркост чињеници да је откривена пре више од девет деценија, ова техника још увек није остварила свој пун потенцијал. Основни разлог за то је недостатак стандардизације који условљава ограничења у смислу поновљивости и упоредивости између различитих истраживања. Додатно, варијабилност која је присутна у примени различитих препоручених поступака снимања, може смањити интерес за употребу ЕГГ-а код широког опсега потенцијалних корисника. Наш циљ је био да пружимо евалуацију поједностављене методе мерења тј. протокола који укључује само један канал током релативно кратког временског периода (20 минута) у статичким условима са ограниченим кретањем субјекта тј. у мировању. Такође, приказали смо наше ставове у вези најприкладније позиције површинских електрода за ЕГГ снимање. Презентовали смо и резултате испитивања метода, на бази обраде видео снимка као и фракционог диференцијалног рачуна, за отклањање артефаката помераја – једног од највећих изазова са којима је суочена ЕГГ метода. За ЕГГ је уобичајено да се користе дуготрајни протоколи у статичким условима. Наш други циљ био је да представимо и оценимо употребљивост супротног приступа – краткотрајних снимања у динамичким условима. Реализовали смо истраживање на пољу оцене активности желуца током појаве симптома мучнине изазване виртуелном реалношћу и симулацијом вожње. За потребе методе за оцену електричне активности желуца, предложили смо три нова параметра за квантификацију ЕГГ сигнала (ефективну вредност амплитуде, медијану и крест фактор) и извршили процену њихове прикладности за оцену гастроинтестиналног тракта током коришћења виртуелне реалности и симулатора вожње. Закључак је да ЕГГ протокол у статичким условима може бити упрошћен и његово трајање може бити редуковано, док је у динамичким условима могуће снимити одговарајући ЕГГ сигнал, али уз праћење препорука наведених у овој тези. Употребом нових техника за процесирање сигнала и прорачун одговарајућих параметара, ЕГГ може бити корисна техника за оцену мучнине изазване коришћењем симулатора и производа виртуелне реалност

An Adaptive Hilbert-Huang Transform System

This thesis presents a system which can be used to generate Intrinsic Mode Functions and the associated Hilbert spectrum resulting from techniques based on the Empirical Mode Decomposition as pioneered by N. E. Huang at the end of the 20th century. Later dubbed the Hilbert-Huang Transform by NASA, the process of decomposing data manually through repetitive detrending and subtraction followed by applying the Hilbert transform to the results was presented as a viable alternative to the wavelet transform which was gaining traction at the time but had shown significant limitations. In the last 20 years, the Hilbert-Huang Transform has received a lot of attention, but that attention has been miniscule relative to the amount of attention received by wavelet transformation. This is, in part, due to the limitations of the Empirical Mode Decomposition and also in part due to the difficulty in developing a theoretical basis for the manner in which the Empirical Mode Decomposition works. While the question of theoretical foundations is an important and tricky one, this thesis presents a system that breaks many of the previously known limits on band-width resolution, mode mixing, and viable decomposable frequency range relative to sampling frequency of the Empirical Mode Decomposition. Many recent innovations do not simply improve on N. E. Huang’s algorithm, but rather provide new approaches with different decompositional properties. By choosing the best technique at each step, a superior total decomposition can be arrived at. Using the Hilbert-Huang Transform itself during the decomposition as a guide as suggested by R. Deering in 2005, the final HHT can show distinct improvements. The AHHT System utilizes many of the properties of various Empirical Mode Decomposition techniques from literature, includes some novel innovations on those techniques, and then manages the total decomposition in an adaptive manner. The Adaptive Hilbert-Huang Transform System (AHHT) is demonstrated successfully on many different artificial signals, many with varying levels of noise down to -5dB SNR, as well as on an electrocardiogram and for comparison with a surface electromyographic study which found biopotential frequency-shifting associated with the fatigue of fast-twitch muscle fibers

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...