Analysis of visual evoked potentials through Wiener filtering applied to a small number of sweeps

Assessing the influence of latency variability on EEG classifiers - a case study of face repetition priming

Data-driven strategies have been widely used to distinguish experimental effects on single-trial EEG signals. However, how latency variability, such as within-condition jitter or latency shifts between conditions, affects the performance of EEG classifiers has not been well investigated. Without explicitly considering and disentangling such attributes of single trials, neural network-based classifiers have limitations in measuring their contributions. Inspired by domain knowledge of subcomponent latency and amplitude from traditional cognitive neuroscience, this study applies a stepwise latency correction method on single trials to control for their contributions to classifier behavior. As a case study demonstrating the value of this method, we measure repetition priming effects of faces, which induce large reaction time differences, latency shifts, and amplitude effects in averaged event-related potentials. The results show that within-condition jitter negatively impacts classifier performance, but between-condition latency shifts improve accuracy, whereas genuine amplitude differences have no significant influence. While demonstrated in the case of priming effects, this methodology can be generalized to experiments involving many kinds of time-varying signals to account for the contributions of latency variability to classifier performance.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-024-10181-2.

ETucker: a constrained tensor decomposition for single trial ERP extraction

Objective.In this paper, we propose a new tensor decomposition to extract event-related potentials (ERP) by adding a physiologically meaningful constraint to the Tucker decomposition.Approach.We analyze the performance of the proposed model and compare it with Tucker decomposition by synthesizing a dataset. The simulated dataset is generated using a 12th-order autoregressive model in combination with independent component analysis (ICA) on real no-task electroencephalogram (EEG) recordings. The dataset is manipulated to contain the P300 ERP component and to cover different SNR conditions, ranging from 0 to -30 dB, to simulate the presence of the P300 component in extremely noisy recordings. Furthermore, in order to assess the practicality of the proposed methodology in real-world scenarios, we utilized the brain-computer interface (BCI) competition III-dataset II.Main results.Our primary results demonstrate the superior performance of our approach compared to conventional methods commonly employed for single-trial estimation. Additionally, our method outperformed both Tucker decomposition and non-negative Tucker decomposition in the synthesized dataset. Furthermore, the results obtained from real-world data exhibited meaningful performance and provided insightful interpretations for the extracted P300 component.Significance.The findings suggest that the proposed decomposition is eminently capable of extracting the target P300 component's waveform, including latency and amplitude as well as its spatial location, using single-trial EEG recordings.

Averaging methods for extracting representative waveforms from motor unit action potential trains

In the context of quantitative electromyography (EMG), it is of major interest to obtain a waveform that faithfully represents the set of potentials that constitute a motor unit action potential (MUAP) train. From this waveform, various parameters can be determined in order to characterize the MUAP for diagnostic analysis. The aim of this work was to conduct a thorough, in-depth review, evaluation and comparison of state-of-the-art methods for composing waveforms representative of MUAP trains. We evaluated nine averaging methods: Ensemble (EA), Median (MA), Weighted (WA), Five-closest (FCA), MultiMUP (MMA), Split-sweep median (SSMA), Sorted (SA), Trimmed (TA) and Robust (RA) in terms of three general-purpose signal processing figures of merit (SPMF) and seven clinically-used MUAP waveform parameters (MWP). The convergence rate of the methods was assessed as the number of potentials per MUAP train (NPM) required to reach a level of performance that was not significantly improved by increasing this number. Test material comprised 78 MUAP trains obtained from the tibialis anterioris of seven healthy subjects. Error measurements related to all SPMF and MWP parameters except MUAP amplitude descended asymptotically with increasing NPM for all methods. MUAP amplitude showed a consistent bias (around 4% for EA and SA and 1-2% for the rest). MA, TA and SSMA had the lowest SPMF and MWP error figures. Therefore, these methods most accurately preserve and represent MUAP physiological information of utility in clinical medical practice. The other methods, particularly WA, performed noticeably worse. Convergence rate was similar for all methods, with NPM values averaged among the nine methods, which ranged from 10 to 40, depending on the waveform parameter evaluated.

Complex tensor based blind source separation of EEG for tracking P300 subcomponents

Complex tensor factorisation of correlated brain sources is addressed in this paper. The electrical brain responses due to motory, sensory, or cognitive stimuli, i.e. event related potentials (ERPs), particularly P300, have been used for cognitive information processing. P300 has two subcomponents, P3a and P3b which are correlated and therefore, the traditional blind source separation approaches cannot solve the problem. In this work, a complex-valued tensor factorisation of electroencephalography (EEG) signals is introduced with the aim of separating P300 subcomponents. The proposed method uses complex-valued statistics to exploit the data correlation. In this way, the variations of P3a and p3b can be tracked for the assessment of the brain state. The results of this work will be compared with those of spatial principal component analysis (SPCA) method.

Acoustic cardiac signals analysis: a Kalman filter-based approach

Auscultation of the heart is accompanied by both electrical activity and sound. Heart auscultation provides clues to diagnose many cardiac abnormalities. Unfortunately, detection of relevant symptoms and diagnosis based on heart sound through a stethoscope is difficult. The reason GPs find this difficult is that the heart sounds are of short duration and separated from one another by less than 30 ms. In addition, the cost of false positives constitutes wasted time and emotional anxiety for both patient and GP. Many heart diseases cause changes in heart sound, waveform, and additional murmurs before other signs and symptoms appear. Heart-sound auscultation is the primary test conducted by GPs. These sounds are generated primarily by turbulent flow of blood in the heart. Analysis of heart sounds requires a quiet environment with minimum ambient noise. In order to address such issues, the technique of denoising and estimating the biomedical heart signal is proposed in this investigation. Normally, the performance of the filter naturally depends on prior information related to the statistical properties of the signal and the background noise. This paper proposes Kalman filtering for denoising statistical heart sound. The cycles of heart sounds are certain to follow first-order Gauss–Markov process. These cycles are observed with additional noise for the given measurement. The model is formulated into state-space form to enable use of a Kalman filter to estimate the clean cycles of heart sounds. The estimates obtained by Kalman filtering are optimal in mean squared sense.

A subspace method for dynamical estimation of evoked potentials

It is a challenge in evoked potential (EP) analysis to incorporate prior physiological knowledge for estimation. In this paper, we address the problem of single-channel trial-to-trial EP characteristics estimation. Prior information about phase-locked properties of the EPs is assesed by means of estimated signal subspace and eigenvalue decomposition. Then for those situations that dynamic fluctuations from stimulus-to-stimulus could be expected, prior information can be exploited by means of state-space modeling and recursive Bayesian mean square estimation methods (Kalman filtering and smoothing). We demonstrate that a few dominant eigenvectors of the data correlation matrix are able to model trend-like changes of some component of the EPs, and that Kalman smoother algorithm is to be preferred in terms of better tracking capabilities and mean square error reduction. We also demonstrate the effect of strong artifacts, particularly eye blinks, on the quality of the signal subspace and EP estimates by means of independent component analysis applied as a prepossessing step on the multichannel measurements.

Tracking single-trial evoked potential changes with Kalman filtering and smoothing

A mathematical way to describe trial-to-trial variations in evoked potentials (EPs) is given by state-space modeling. Linear estimators optimal in the mean square sense can then be obtained through Kalman filter and smoother algorithms. Of importance are the parametrization of the problem and the selection of an observation model for estimation. In this paper, we introduce a general way for designing a model for dynamical estimation of EPs. The observation model is constructed based on a finite impulse response (FIR) filter and can be used for different kind of EPs. We also demonstrate that for batch processing the use of the smoother algorithm is preferable. The method is demonstrated with measurements obtained from an experiment with visual stimulation.

Single-Trial Dynamical Estimation of Event-Related Potentials: A Kalman Filter-Based Approach

A method for single-trial dynamical estimation of event-related potentials (ERPs) is presented. The method is based on recursive Bayesian mean square estimation and the estimators are obtained with a Kalman filtering procedure. We especially focus on the case that previous trials contain prior information of relevance to the trial being analyzed. The potentials are estimated sequentially using the previous estimates as prior information. The performance of the method is evaluated with simulations and with real P300 responses measured using auditory stimuli. Our approach is shown to have excellent capability of estimating dynamic changes form stimulus to stimulus present in the parameters of the ERPs, even in poor signal-to-noise ratio (SNR) conditions.

A Bayesian approach to estimate evoked potentials

Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for improving the measurement of evoked potentials (EP) performed by conventional averaging (CA). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd-order statistical information on the background EEG and on the unknown EP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible (i.e. it can be employed for a large class of EP) and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. The mean EP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error, a quantity determinable thanks to the employment of the Bayesian approach. The performance of the new approach is shown on both simulated and real auditory EP. A signal-to-noise ratio enhancement is obtained that can allow the (possibly automatic) identification of peak latencies and amplitudes with less sweeps than those required by CA. For cochlear EP, the method also allows the audiology investigator to gather new and clinically important information. The possibility of handling single-sweep analysis with further development of the method is also addressed.

The feasibility of maximum length sequences to reduce acquisition time of the middle latency response

Maximum length sequences (MLS) have been used to improve the signal-to-noise ratio (SNR) of otoacoustic emissions [Thornton, J. Acoust. Soc. Am. 94, 132-136 (1993)] and the auditory brainstem response [Thornton and Slaven, Br. J. Audiol. 27, 205-210 (1993)]. By implication, a shorter recording time would be required to give equal signal-to-noise ratio (SNR). This study aimed to establish whether it is also possible to improve the SNR of the auditory-evoked potential termed the middle latency response (MLR) using maximum length sequences (MLS). Recordings of 180 s each were made using a conventional recording rate and MLS rates of 42, 89, and 185 clicks/s. Three different stimulus intensities were used in the range 30 to 70 dB nHL. The rate of 89 clicks/s was found to produce most improvement in SNR for both the Na-Pa region of the MLR and the Na-Pb region. This improvement in SNR using MLS implies that an MLS rate of 89 clicks/s would produce a fourfold reduction in recording time for equal SNR over conventional recording for the Pa-Nb region of the MLR at a stimulus intensity of 70 dB nHL. The latency of the Nb wave was found to reduce significantly using MLS. An MLR could not be recorded from every subject in this study, but more subjects had an identifiable response for MLS than for conventional recordings. Use of MLS to record the MLR appears to offer the potential for reduction in test time and better wave identification.

Bispectrum analysis of focal ischemic cerebral EEG signal using third-order recursion method

In this paper, a model for Sprague-Dawley (SD) rat focal ischemic cerebral injury is presented. Based on this experimental model, the electroencephalogram (EEG) from the ischemic region and from a normal region are collected during the first 30 min of ischemia. The EEG bispectrum analysis is carefully investigated by using the third-order recursion method. We found that some characteristics of the bispectrum are very sensitive to focal ischemic cerebral injury. The maximum magnitude and the weighted center of EEG bispectrum (WCOB) change according to the extent and the place of the injury region. The bispectrum analysis results have been verified by the heat shock protein (HSP) test. The study indicates that the EEG bispectrum analysis may be useful to distinguish the ischemic region from the normal one and to estimate the ischemic extent.

Selecting relevant electrode positions for classification tasks based on the electro-encephalogram

The aim is to describe a general approach to determining important electrode positions when measured electro-encephalogram signals are used for classification. The approach is exemplified in the frame of the brain-computer interface, which crucially depends on the classification of different brain states. To classify two brain states, e.g. planning of movement of right and left index fingers, three different approaches are compared: classification using a physiologically motivated set of four electrodes, a set determined by principal component analysis and electrodes determined by spatial pattern analysis. Spatial pattern analysis enhances the classification rate significantly from 61.3 +/- 1.8% (with four electrodes) to 71.8 +/- 1.4%, whereas the classification rate using principal component analysis is significantly lower (65.2 +/- 1.4%). Most of the 61 electrodes used have no influence on the classification rate, so that, in future experiments, the setup can be simplified drastically to six to eight electrodes without loss of information.

Subspace regularization method for the single-trial estimation of evoked potentials

A method for the single-trial estimation of the evoked potentials is proposed. The method is based on the so-called subspace regularization approach in which the second-order statistics of the set of the measurements is used to form a prior information model for the evoked potentials. The method is closely related to the Bayesian estimation. The performance of the proposed method is evaluated using realistic simulations. As a specific application the method is applied to the estimation of the target responses in the P300 test.

Estimation of single event-related potentials utilizing the Prony method

This paper deals with estimation of the waveform of a single event-related potential, sERP. An additive noise model is used for the measured signal and the SNR of the disturbed sERP is approximately 0 dB. The sERP is described by a series expansion where the basis functions are damped sinusoids. The fundamental basis function is estimated by the least squares Prony method, derived for colored noise. The performance of the Prony method for different forms of the power density spectrum of the noise is investigated. A white noise approximation can be used at a low signal-to-noise (SNR). The basis functions change slowly but the waveform of the sERP may vary from one stimulus to another, thus we average a small number of correlation functions in order to increase the SNR. The method is evaluated by using measurements from four subjects and the results confirm the variability of the sERP.

Dynamic extraction of visual evoked potentials through spatial analysis and dipole localization

The dynamic extraction of evoked potential is a problem of great interest in EEG signal processing. In this paper, a comprehensive method is presented which integrates spatial analysis and dipole localization to make full use of the spatial-temporal information contained in the multichannel stimulation records. A realistic double boundary head model is constructed through CT scans and a two-step method devised to overcome the ill-posed nature of the forward problem of EEG caused by the low conductivity of the skull. As a result, visual evoked potentials can be effectively extracted from only two consecutive records and the dynamic information of visual evoked potential thus procured. The efficiency of the presented method has been verified by means of computer simulation and a clinical experiment.

Some considerations on estimating event-related brain signals

Understanding the timing of mental acts is one of the prominent questions in information processing research. The analysis of event related potentials (ERP) with their high temporal resolution might make access to cognition related brain activity possible. We consider three major problems which make the application of ERPs questionable and then propose some solutions to these problems. The primary problem concerns the separation of the ERPs from the background EEG which is not related to the stimulus. The most common method used is averaging. We argue that this is not the most appropriate method and suggest an alternative for estimating the signal in single-trial recordings. Artifacts present a second problem. We will first review established methods of dealing with eye-movement artifacts and then propose an alternative. We will also report on current work on the parametrisation of single-trial signal estimates, which constitute the third problem considered.

Single P100 visual evoked potential analyses in man

Standards evoked potential averaging leads to a loss of information inherent in the moment to moment variability of the amplitude and latency of single evoked potentials. In order to extract this information, attempts were made to develop procedures which would allow recording of single visual evoked potentials in at least a selected group of subjects. In 11 out of 25 non-selected subjects, 43% to 86% of all stimuli (reversal checkerboard pattern elicited single visual evoked potentials (VEP) which were recognized as such by a group of independent observers. The mean amplitude and latency obtained by directly measuring the peak to peak amplitudes and peak latencies of these single VEPs (arithmetic averaging) were compared to those obtained following conventional time-locked averaging of the same data. During long-term continuous stimulation, the arithmetic averaged VEPs increased in amplitude to a steady state while the time-locked averages of the same sets of responses decreased in amplitude. This reduction was found to be closely related to the latency jitter. It may provide a better understanding of the phenomenon of habituation. This finding was confirmed in model single VEPs obtained by summing on-going pre-stimulus EEG activity with a time-locked average VEP stationary wave form. The variability of the true single VEPs was found to be less than the variability of the model single VEPs. The latency and amplitude parameters of the true single VEPs were strongly correlated with each other while those of the model single VEPs were not. These findings show that single VEPs have an inherent variability which may reflect brain processing.

A model for the cortico-cortical neural interaction in multisensory-evoked potentials

This paper addresses the methodological problem of enhancing selective responses from the central nervous system when two (or more) different sensorial stimuli are simultaneously presented to the subject. In particular, contemporaneous visual and somato-sensory stimulation is considered and a model of signal and noise interaction is developed for the processing of the evoked responses. An ARXX parametric model (AutoRegressive with two eXogenous inputs) is introduced and a least squares algorithm is used to determine the selective response of the two neural systems from the overall evoked response. Such an analysis may be also carried out on a sweep-by-sweep basis. Applications of this method are the following ones: i) modeling of multisensory potentials; ii) description of facilitation or defacilitation phenomena in multitasking experiments; iii) analysis of cortico-cortical neural interactions.

Parametric method for the detection of inter- and intrasweep variability in VEP processing

The paper introduces a Kalman filter procedure for the processing of single-sweep visual evoked potentials (VEPs). The identification of the filter coefficients is based on a model of signal and noise interaction which considers the generating process as the superposition of the true evoked response to an AR process (the background EEG) and a broader spectrum noise. Intersweep variability is thus evident on the filtered response and a functional parameter of the filter (VP(t), namely variability path) is proposed for the automatic determination of the latencies associated with the main peaks of the response. Finally, the time-variant algorithm allows the quantification of the intrasweep variability for possible interpretation of the physiological mechanism involved.

The implementation of an autoregressive model with exogenous input in a single sweep visual evoked potential analysis

Based on a model of signal-noise interaction, we present a method for single-sweep analysis of Visual Evoked Potentials. The EEG is represented as an autoregressive process and the single-sweep VEP as a filtered version of a reference signal taken as the running average of 20 consecutive sweeps. The algorithm for model identification and filtering is an ARX (AutoRegressive with eXogenous input) which provides a fast and efficient solution by means of a least squares approach. The choice of reference signal, as well as the complexity of the model, is also discussed. A further advantage of this approach is parameter reduction: all the single-sweep information is contained in 18 model coefficients and the reference signal.