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

Advancing Brain-Computer Interface Systems: Asynchronous Classification of Error Potentials

This paper explores the paradigm shift in the classification of Error-Related Potentials (ErrP) in Brain-Computer Interfaces (BCIs) by introducing an asynchronous approach. Traditional synchronous methods, relying on precise temporal alignment between stimuli presentation and neural responses, face challenges in real-world scenarios with human response variability.The proposed asynchronous classification liberates BCI systems from strict temporal constraints, allowing for a more natural interaction paradigm. The study introduces an innovative ensemble method comprising Linear Discriminant Analysis (LDA) and EEGNet for asynchronous ErrP classification.The method is evaluated on EEG data from the BNCI Horizon 2020 dataset, demonstrating high balanced accuracy. While the introduction of EEGNet refines the classification, reducing false positives, challenges persist in achieving a balanced trade-off between precision and recall.The findings suggest the ensemble method's potential for practical applications, emphasizing the need for further refinement and exploration of advanced techniques in asynchronous ErrP classification.

Domain-Specific Processing Stage for Estimating Single-Trail Evoked Potential Improves CNN Performance in Detecting Error Potential

We present a novel architecture designed to enhance the detection of Error Potential (ErrP) signals during ErrP stimulation tasks. In the context of predicting ErrP presence, conventional Convolutional Neural Networks (CNNs) typically accept a raw EEG signal as input, encompassing both the information associated with the evoked potential and the background activity, which can potentially diminish predictive accuracy. Our approach involves advanced Single-Trial (ST) ErrP enhancement techniques for processing raw EEG signals in the initial stage, followed by CNNs for discerning between ErrP and NonErrP segments in the second stage. We tested different combinations of methods and CNNs. As far as ST ErrP estimation is concerned, we examined various methods encompassing subspace regularization techniques, Continuous Wavelet Transform, and ARX models. For the classification stage, we evaluated the performance of EEGNet, CNN, and a Siamese Neural Network. A comparative analysis against the method of directly applying CNNs to raw EEG signals revealed the advantages of our architecture. Leveraging subspace regularization yielded the best improvement in classification metrics, at up to 14% in balanced accuracy and 13.4% in F1-score.

An EEG Classification-Based Method for Single-Trial N170 Latency Detection and Estimation

Event-related potentials (ERPs) can reflect the high-level thinking activities of the brain. In ERP analysis, the superposition and averaging method is often used to estimate ERPs. However, the single-trial ERP estimation can provide researchers with more information on cognitive activities. In recent years, more and more researchers try to find an effective method to extract single-trial ERPs, because most of the existing methods have poor generalization ability or suffer from strong assumptions about the characteristics of ERPs, resulting in unsatisfactory results under the condition of a very low signal-to-noise ratio. In this paper, an EEG classification-based method for single-trial ERP detection and estimation was proposed. This study used a linear generated EEG model containing templates of ERP local descriptors which include amplitude and latency, and this model can avoid the invalid assumption about ERPs taken by other methods. The purpose of this method is not to recover the whole ERP waveform but to model the amplitude and latency of ERP components. This method afterwards examined the three machine learning models including logistic regression, neural network, and support vector machine in the EEG signal classification for ERP detection and selected the best performed MLPNN model for detection. To get the utmost out of information produced in the classification process, this study also used extra information to propose a new optimization model, with which outperformed detection results were obtained. Performance of the proposed method is evaluated on simulated N170 and real P50 data sets, and the results show that the model is more effective than the Woody filter and the SingleTrialEM algorithm. These results are also consistent with the conclusion of sensory gating, which demonstrated good generalization ability.

Single-trial event-related potential extraction through one-unit ICA-with-reference

OBJECTIVE

In recent years, ICA has been one of the more popular methods for extracting event-related potential (ERP) at the single-trial level. It is a blind source separation technique that allows the extraction of an ERP without making strong assumptions on the temporal and spatial characteristics of an ERP. However, the problem with traditional ICA is that the extraction is not direct and is time-consuming due to the need for source selection processing. In this paper, the application of an one-unit ICA-with-Reference (ICA-R), a constrained ICA method, is proposed.

APPROACH

In cases where the time-region of the desired ERP is known a priori, this time information is utilized to generate a reference signal, which is then used for guiding the one-unit ICA-R to extract the source signal of the desired ERP directly.

MAIN RESULTS

Our results showed that, as compared to traditional ICA, ICA-R is a more effective method for analysing ERP because it avoids manual source selection and it requires less computation thus resulting in faster ERP extraction.

SIGNIFICANCE

In addition to that, since the method is automated, it reduces the risks of any subjective bias in the ERP analysis. It is also a potential tool for extracting the ERP in online application.

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.

A joint sparse representation-based method for double-trial evoked potentials estimation

In this paper, we present a novel approach to solving an evoked potentials estimating problem. Generally, the evoked potentials in two consecutive trials obtained by repeated identical stimuli of the nerves are extremely similar. In order to trace evoked potentials, we propose a joint sparse representation-based double-trial evoked potentials estimation method, taking full advantage of this similarity. The estimation process is performed in three stages: first, according to the similarity of evoked potentials and the randomness of a spontaneous electroencephalogram, the two consecutive observations of evoked potentials are considered as superpositions of the common component and the unique components; second, making use of their characteristics, the two sparse dictionaries are constructed; and finally, we apply the joint sparse representation method in order to extract the common component of double-trial observations, instead of the evoked potential in each trial. A series of experiments carried out on simulated and human test responses confirmed the superior performance of our method.

A multi-task learning approach for the extraction of single-trial evoked potentials

Evoked potentials (EPs) are of great interest in neuroscience, but their measurement is difficult as they are embedded in background spontaneous electroencephalographic (EEG) activity which has a much larger amplitude. The widely used averaging technique requires the delivery of a large number of identical stimuli and yields only an "average" EP which does not allow the investigation of the possible variability of single-trial EPs. In the present paper, we propose the use of a multi-task learning method (MTL) for the simultaneous extraction of both the average and the N single-trial EPs from N recorded sweeps. The technique is developed within a Bayesian estimation framework and uses flexible stochastic models to describe the average response and the N shifts between the single-trial EPs and this average. Differently from other single-trial estimation approaches proposed in the literature, MTL can provide estimates of both the average and the N single-trial EPs in a single stage. In the present paper, MTL is successfully assessed on both synthetic (100 simulated recording sessions with N=20 sweeps) and real data (11 subjects with N=20 sweeps) relative to a cognitive task carried out for the investigation of the P300 component of the EP.

Improving the efficacy of ERP-based BCIs using different modalities of covert visuospatial attention and a genetic algorithm-based classifier

We investigated whether the covert orienting of visuospatial attention can be effectively used in a brain-computer interface guided by event-related potentials. Three visual interfaces were tested: one interface that activated voluntary orienting of visuospatial attention and two interfaces that elicited automatic orienting of visuospatial attention. We used two epoch classification procedures. The online epoch classification was performed via Independent Component Analysis, and then it was followed by fixed features extraction and support vector machines classification. The offline epoch classification was performed by means of a genetic algorithm that permitted us to retrieve the relevant features of the signal, and then to categorise the features with a logistic classifier. The offline classification, but not the online one, allowed us to differentiate between the performances of the interface that required voluntary orienting of visuospatial attention and those that required automatic orienting of visuospatial attention. The offline classification revealed an advantage of the participants in using the "voluntary" interface. This advantage was further supported, for the first time, by neurophysiological data. Moreover, epoch analysis was performed better with the "genetic algorithm classifier" than with the "independent component analysis classifier". We suggest that the combined use of voluntary orienting of visuospatial attention and of a classifier that permits feature extraction ad personam (i.e., genetic algorithm classifier) can lead to a more efficient control of visual BCIs.

Clustering linear discriminant analysis for MEG-based brain computer interfaces

In this paper, we propose a clustering linear discriminant analysis algorithm (CLDA) to accurately decode hand movement directions from a small number of training trials for magnetoencephalography-based brain computer interfaces (BCIs). CLDA first applies a spectral clustering algorithm to automatically partition the BCI features into several groups where the within-group correlation is maximized and the between-group correlation is minimized. As such, the covariance matrix of all features can be approximated as a block diagonal matrix, thereby facilitating us to accurately extract the correlation information required by movement decoding from a small set of training data. The efficiency of the proposed CLDA algorithm is theoretically studied and an error bound is derived. Our experiment on movement decoding of five human subjects demonstrates that CLDA achieves superior decoding accuracy over other traditional approaches. The average accuracy of CLDA is 87% for single-trial movement decoding of four directions (i.e., up, down, left, and right).

Single-trial subspace-based approach for VEP extraction

A signal subspace approach for extracting visual evoked potentials (VEPs) from the background electroencephalogram (EEG) colored noise without the need for a prewhitening stage is proposed. Linear estimation of the clean signal is performed by minimizing signal distortion while maintaining the residual noise energy below some given threshold. The generalized eigendecomposition of the covariance matrices of a VEP signal and brain background EEG noise is used to transform them jointly to diagonal matrices. The generalized subspace is then decomposed into signal subspace and noise subspace. Enhancement is performed by nulling the components in the noise subspace and retaining the components in the signal subspace. The performance of the proposed algorithm is tested with simulated and real data, and compared with the recently proposed signal subspace techniques. With the simulated data, the algorithms are used to estimate the latencies of P(100), P(200), and P(300) of VEP signals corrupted by additive colored noise at different values of SNR. With the real data, the VEP signals are collected at Selayang Hospital, Kuala Lumpur, Malaysia, and the capability of the proposed algorithm in detecting the latency of P(100) is obtained and compared with other subspace techniques. The ensemble averaging technique is used as a baseline for this comparison. The results indicated significant improvement by the proposed technique in terms of better accuracy and less failure rate.

Comparison of methods for optimal choice of the regularization parameter for linear electrical impedance tomography of brain function

Electrical impedance tomography has the potential to provide a portable non-invasive method for imaging brain function. Clinical data collection has largely been undertaken with time difference data and linear image reconstruction methods. The purpose of this work was to determine the best method for selecting the regularization parameter of the inverse procedure, using the specific application of evoked brain activity in neonatal babies as an exemplar. The solution error norm and image SNR for the L-curve (LC), discrepancy principle (DP), generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) selection methods were evaluated in simulated data using an anatomically accurate finite element method (FEM) of the neonatal head and impedance changes due to blood flow in the visual cortex recorded in vivo. For simulated data, LC, GCV and UPRE were equally best. In human data in four neonatal infants, no significant differences were found among selection methods. We recommend that GCV or LC be employed for reconstruction of human neonatal images, as UPRE requires an empirical estimate of the noise variance.

Enhanced detection of visual-evoked potentials in brain-computer interface using genetic algorithm and cyclostationary analysis

We propose a novel framework to reduce background electroencephalogram (EEG) artifacts from multitrial visual-evoked potentials (VEPs) signals for use in brain-computer interface (BCI) design. An algorithm based on cyclostationary (CS) analysis is introduced to locate the suitable frequency ranges that contain the stimulus-related VEP components. CS technique does not require VEP recordings to be phase locked and exploits the intertrial similarities of the VEP components in the frequency domain. The obtained cyclic frequency spectrum enables detection of VEP frequency band. Next, bandpass or lowpass filtering is performed to reduce the EEG artifacts using these identified frequency ranges. This is followed by overlapping band EEG artifact reduction using genetic algorithm and independent component analysis (G-ICA) which uses mutual information (MI) criterion to separate EEG artifacts from VEP. The CS and GA methods need to be applied only to the training data; for the test data, the knowledge of the cyclic frequency bands and unmixing matrix would be sufficient for enhanced VEP detection. Hence, the framework could be used for online VEP detection. This framework was tested with various datasets and it showed satisfactory results with very few trials. Since the framework is general, it could be applied to the enhancement of evoked potential signals for any application.

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.

Composite Noise Reduction of ERPs Using Wavelet, Model-Based, and Principal Component Subspace Methods

This paper used three theoretically different algorithms for reducing noise in event-related potential (ERP) data. It examined the possibility that a hybrid of these methods could show gains in noise reduction beyond that obtained with any single method. The well-known ERP oddball paradigm was used to evaluate three denoising methods: statistical wavelet transform (wavelet-Z), a smooth subspace wavelet filter (wavelet-S), and subspace PCA. The six possible orders of serial application of these methods to the oddball waveforms were compared for efficacy in signal enhancement. It was found that the order was not commutative, with the best results obtained from applying the wavelet-Z first. Comparison of oddball and frequent trials in the grand average and in individual averages showed considerable enhancement of the differences. It was concluded that denoising to remove variance caused by rare sizeable artifacts is best done first, followed by state space PCA and a light-bias model-based wavelet denoising. The ability to detect and distinguish the effects of variables (such as task, drug effects, individual differences, etc.) on ERPs related to human cognition could be considerably advanced using the denoising methods described here.

Estimation of single-trial fMRI BOLD responses using combined EEG and fMRI measurements

In this paper, we present a method for modeling human brain response using combined fMRI and EEG measurements. A subspace is formed using the eigenvectors of data correlation matrix of augmented measurements. This subspace is then used for regularization of the fitting of parametric model to fMRI BOLD signal. The approach is utilized for single-trial estimation of blood oxygenation level dependent (BOLD) responses in fMRI time series.

On correlation between single-trial ERP and GSR responses: a principal component regression approach

In this study we investigate the correlation between single-trial evoked brain responses and galvanic skin responses (GSR). The correlation between the two signals is examined by using a modified principal component regression based approach. A potential application of the study is to utilize the GSR measurements in a form of a prior information in the estimation of the brain potentials when only small number of trials is available.

Comparing a template approach and complex bandpass filtering for single-trial analysis of auditory evoked M100

Two methods for single-trial analysis were compared, an established parametric template approach and a recently proposed non-parametric method based on complex bandpass filtering. The comparison was carried out by means of pseudo-real simulations based on magnetoencephalography measurements of cortical responses to auditory signals. The comparison focused on amplitude and latency estimation of the M100 response. The results show that both methods are well suited for single-trial analysis of the auditory evoked M100. While both methods performed similarly with respect to latency estimation, the non-parametric approach was observed to be more robust for amplitude estimation. The non-parametric approach can thus be recommended as an additional valuable tool for single-trial analysis.

Extracting ERP by combination of subspace method and lift wavelet transform

Event Related Potentials (ERP) recorded from the scalp include various noises. The main source of the noise is the spontaneous brain activity and it is called the background Electroencephalography (EEG). Because EEG is highly colored, we wouldn't effectively remove EEG noise by wavelet transform. This paper proposed a new approach that combined the subspace method and lift wavelet transform in order to reduce the number of trials required for the extraction of the brain Event Related Potentials. First, the signal subspace is estimated by applying the singular value decomposition (SVD). Orthonormal projecting the raw data onto the estimated signal subspace can obtain a pre-denoised signal and it whitened the colored noise. Next, the ERPs are extracted by lift wavelet construction of the enhanced version. Simulation results show that the combination of both two methods provides much better capability than each of them separately.

Subspace approaches for FMRI time series estimation

In this paper, we present a subspace approach for functional magnetic resonance imaging (fMRI) time series analysis. The signal subspace is formed of the eigenvectors of data correlation matrix. The approach is utilized both for single-trial estimation of blood oxygenation level dependent (BOLD) responses in fMRI time series and for studying the functional connectivity of BOLD responses from different spatial areas.

Relationship of P300 single-trial responses with reaction time and preceding stimulus sequence

Variation of single-trial P300 responses was studied both in relation to reaction times and to the preceding stimulus sequence in an auditory oddball paradigm. Single-trial responses were estimated with the Subspace regularization method that is based on Bayesian estimation and linear modeling. The results of the single-trial method were compared to those of averaging. Both methods showed that the latency of the P300 was shorter and its amplitude larger for faster than slower reaction times. The P300 latency was shorter for target tones that were preceded by a large number of standard tones compared to those preceded by a small number of standard tones. The P300 amplitude was statistically significantly affected by the stimulus sequence only when analyzed with conventional averaging. In-depth analysis of standard deviations showed that the variability of the P300 single-trial latencies could explain the differences between the two methods. Specifically, the regression analysis showed that the latency correlated negatively with the number of preceding standard tones and positively with the reaction time, whereas the P300 amplitude correlated positively with the number of the preceding standard stimuli and negatively with the reaction time. The analysis of the single-trial responses gives information about the behavior of the P300 component that is lost with conventional averaging. The method used in this study is independent of subjective decision making and can be used to model changes in the dynamical behavior of the P300 component objectively.

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 template-free approach for determining the latency of single events of auditory evoked M100

The phase of the complex output of a narrow band Gaussian filter is taken to define the latency of the auditory evoked response M100 recorded by magnetoencephalography. It is demonstrated that this definition is consistent with the conventional peak latency. Moreover, it provides a tool for reducing the number of averages needed for a reliable estimation of the latency. Single-event latencies obtained by this procedure can be used to improve the signal quality of the conventional average by latency adjusted averaging.

Geometrical interpretation of fMRI-guided MEG/EEG inverse estimates

Magneto- and electroencephalography (MEG/EEG) and functional magnetic resonance imaging (fMRI) provide complementary information about the functional organization of the human brain. An important advantage of MEG/EEG is the millisecond time resolution in detecting electrical activity in the cerebral cortex. The interpretation of MEG/EEG signals, however, is limited by the difficulty of determining the spatial distribution of the neural activity. Functional MRI can help in the MEG/EEG source analysis by suggesting likely locations of activity. We present a geometric interpretation of fMRI-guided inverse solutions in which the MEG/EEG source estimate minimizes a distance to a subspace defined by the fMRI data. In this subspace regularization (SSR) approach, the fMRI bias does not assume preferred amplitudes for MEG/EEG sources, only locations. Characteristic dependence of the source estimates on the regularization parameters is illustrated with simulations. When the fMRI locations match the true MEG/EEG source locations, they serve to bias the underdetermined MEG/EEG inverse solution toward the fMRI loci. Importantly, when the fMRI loci do not match the true MEG/EEG loci, the solution is insensitive to those fMRI loci.

Single-trial estimation of multichannel evoked-potential measurements

A method for single-trial estimation of multichannel evoked potentials is presented. The proposed method is based on the regularized least squares scheme. The spatial correlation between the channels is used as additional information in the estimation procedure. Amplitude estimates obtained with the proposed method is compared with the estimates calculated without using the spatial information. The performance of the method is evaluated using simulated and real data of P300 responses measured using auditory stimuli. The multichannel approach is shown to give realistic and comparable information about the amplitude differences of the P300 peak between different channels.

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.