Local polynomial modeling of time-varying autoregressive models with application to time-frequency analysis of event-related EEG

This paper proposes a new local polynomial modeling (LPM) method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG). The LPM method models the TVAR coefficients locally by polynomials and estimates the polynomial coefficients using weighted least-squares with a window having a certain bandwidth. A data-driven variable bandwidth selection method is developed to determine the optimal bandwidth that minimizes the mean squared error. The resultant time-varying power spectral density estimation of the signal is capable of achieving both high time resolution and high frequency resolution in the time-frequency domain, making it a powerful TFA technique for nonstationary biomedical signals like ER-EEG. Experimental results on synthesized signals and real EEG data show that the LPM method can achieve a more accurate and complete time-frequency representation of the signal. © 2006 IEEE.published_or_final_versio

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method

Local polynomial modelling of time-varying autoregressive processes and its application to the analysis of event-related electroencephalogram

This paper proposes a new method for identification of time-varying autoregressive (TVAR) models based on local polynomial modeling (LPM) and applies it to investigate the dynamic spectral information of event-related electroencephalogram (EEG). The proposed method models the TVAR coefficients locally by polynomials and estimates those using least-squares estimation with a kernel having a certain bandwidth. A data-driven variable bandwidth selection method is developed to obtain the optimal bandwidth, which minimizes the mean squared error (MSE). Simulation results show that the LPM-based TVAR identification method outperforms conventional methods for different scenarios. The advantages of the LPM method make it a useful high-resolution timefrequency analysis (TFA) technique for nonstationary biomedical signals like EEG. Experimental results show that the LPM method can reveal more meaningful time-frequency characteristics than wavelet transform. ©2010 IEEE.published_or_final_versionThe IEEE International Symposium on Circuits and Systems (ISCAS 2010), Paris, France, 30 May-2 June 2010. In Proceedings of ISCAS, 2010, p. 3124-312

Measuring Instantaneous Frequency of Local Field Potential Oscillations using the Kalman Smoother

Rhythmic local field potentials (LFPs) arise from coordinated neural activity. Inference of neural function based on the properties of brain rhythms remains a challenging data analysis problem. Algorithms that characterize non-stationary rhythms with high temporal and spectral resolution may be useful for interpreting LFP activity on the timescales in which they are generated. We propose a Kalman smoother based dynamic autoregressive model for tracking the instantaneous frequency (iFreq) and frequency modulation (FM) of noisy and non-stationary sinusoids such as those found in LFP data. We verify the performance of our algorithm using simulated data with broad spectral content, and demonstrate its application using real data recorded from behavioral learning experiments. In analyses of ripple oscillations (100–250 Hz) recorded from the rodent hippocampus, our algorithm identified novel repetitive, short timescale frequency dynamics. Our results suggest that iFreq and FM may be useful measures for the quantification of small timescale LFP dynamics.National Institutes of Health (U.S.) (NIH/NIMH R01 MH59733)National Institutes of Health (U.S.) (NIH/NIHLB R01 HL084502)Massachusetts Institute of Technology (Henry E. Singleton Presidential Graduate Fellowship Award

Parametric Modelling of EEG Data for the Identification of Mental Tasks

Electroencephalographic (EEG) data is widely used as a biosignal for the identification of different mental states in the human brain. EEG signals can be captured by relatively inexpensive equipment and acquisition procedures are non-invasive and not overly complicated. On the negative side, EEG signals are characterized by low signal-to-noise ratio and non-stationary characteristics, which makes the processing of such signals for the extraction of useful information a challenging task.peer-reviewe

Coherence analysis: Methods, solutions and problems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.A coherence function is a measure of the correlation of two signals and may be used as a measure for functional relationship between brain areas. In studying functional relationships, referenced EEG (REEG) coherence analysis yields important new aspects of brain activities, which complement the data obtained by power spectral analysis. However, REEG-based coherence tends to show a false high value due to volume conduction from un correlated sources (VCUS). Existing signal processing methods address this issue using a Fourier coherence function of scalp Laplacian. Although this method has been proved useful to reveal correlation between EEG signals with minimum VCUS effects, it only provides frequency-domain analysis. Since EEG signals are highly non-stationary, it is more appropriate to use time-frequency methods for coherence analysis of scalp Laplacian. Thus this research applies the wavelet transform on coherence analysis of scalp Laplacian. To verify our technique, already recorded EEG data of event related potentials were obtained from a study of two large groups of alcoholic and abstinent alcoholic subjects, performing visual picture-recognition tasks. The proposed coherence method successfully detected time-frequency correlation between EEG signals with minimum VCUS effects. It showed significant spatial specificity and revealed detailed coherence patterns. Some new important results regarding time-frequency characteristics of VCUS effects on wavelet and short-time Fourier transform (STFT) coherence analysis of REEG signals were deduced. The proposed coherence method was also compared to a conventional wavelet coherence method of REEG signals in the study of coherence difference between coherences of alcoholic and abstinent alcoholic EEG signals. Results of this study provided substantial evidence that VCUS effects are not additive and therefore can not be ignored in comparison of different brain states between groups of subjects

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi