Parametric classification of multichannel averaged event-related potentials

This paper focuses on the systematic development of a parametric approach for classifying averaged event-related potentials (ERPs) recorded from multiple channels. It is shown that the parameters of the averaged ERP ensemble can be estimated directly from the parameters of the single-trial ensemble, thus, making it possible to design a class of parametric classifiers without having to collect a prohibitively large number of single-trial ERPs. An approach based on random sampling without replacement is developed to generate a large number of averaged ERP ensembles in order to evaluate the performance of a classifier. A two-class ERP classification problem is considered and the parameter estimation methods are applied to independently design a Gaussian likelihood ratio classifier for each channel. A fusion rule is formulated to classify an ERP using the classification results from all the channels. Experiments using real and simulated ERPs are designed to show that, through the approach developed, parametric classifiers can be designed and evaluated even when the number of averaged ERPs does not exceed the dimension of the ERP vector. Additionally, it is shown that the performance of a majority rule fusion classifier is consistently superior to the rule that selects a single best channel.     

Single-trial processing of event-related potentials using outlierinformation

An approach to extracting single-trial event-related information is described. This approach, called the outlier processing method (OPM), is based on the concept that event-related information is contained in electroencephalogram (EEG) time-series outliers. In particular, the OPM has been effective in extracting motor-related information from single-trial EEG. An investigation into the viability of the OPM was carried out on single-trial EEG data from four subjects. The EEG was collected under two conditions: an active task in which the subject performed a skilled thumb movement and an idle task in which the subject remained alert but did not carry out any motor activity. The results of this investigation demonstrated that consistent single-trial motor related information can be successfully extracted using the OPM     

Estimation of single event-related potentials utilizing the Pronymethod

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 low signal-to-noise (SNR). The basis functions change slowly but the waveform of the sERP may vary from one stimulus to another, thus the authors 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     

On decomposing stimulus and response waveforms in event-related potentials recordings

Event-related potentials (ERPs) reflect the brain activities related to specific behavioral events, and are obtained by averaging across many trial repetitions with individual trials aligned to the onset of a specific event, e.g., the onset of stimulus (s-aligned) or the onset of the behavioral response (r-aligned). However, the s-aligned and r-aligned ERP waveforms do not purely reflect, respectively, underlying stimulus (S-) or response (R-) component waveform, due to their cross-contaminations in the recorded ERP waveforms. Zhang [J. Neurosci. Methods, 80, pp. 49-63, 1998] proposed an algorithm to recover the pure S-component waveform and the pure R-component waveform from the s-aligned and r-aligned ERP average waveforms-however, due to the nature of this inverse problem, a direct solution is sensitive to noise that disproportionally affects low-frequency components, hindering the practical implementation of this algorithm. Here, we apply the Wiener deconvolution technique to deal with noise in input data, and investigate a Tikhonov regularization approach to obtain a stable solution that is robust against variances in the sampling of reaction-time distribution (when number of trials is low). Our method is demonstrated using data from a Go/NoGo experiment about image classification and recognition.     

Source localization of event-related potentials incorporating spatial notch filters

A novel algorithm for the localization of event-related potential (ERP) sources within the brain is proposed here. In this technique, spatial notch filters are developed to exploit the multichannel electroencephalogram data together with a model of ERP with variable parameters in order to accurately localize the corresponding ERP signal sources. The algorithm is robust in the presence of reasonably high noise. The performance of the proposed system has been compared to that of linear constrained minimum variance (LCMV) beamformer for different noise and correlation levels and its superiority has been demonstrated.      

Topographic components model for event-related potentials and some biophysical considerations

Models for decomposing averaged event-related potentials in component functions are discussed. Biophysical considerations motivate a sample model, which is shown to lead to unique identifiable components, thereby overcoming a major drawback of the customary approach by principal components analysis.<>     

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.     

Overcoming selective ensemble averaging: unsupervised identification of event-related brain potentials

We present a novel approach to the problem of event-related potential (ERP) identification, based on a competitive artificial neural network (ANN) structure. Our method uses ensembled electroencephalogram (EEG) data just as used in conventional averaging, however without the need for a priori data subgrouping into distinct categories (e.g., stimulus- or event-related), and thus avoids conventional assumptions on response invariability. The competitive ANN, often described as a winner takes all neural structure, is based on dynamic competition among the net neurons where learning takes place only with the winning neuron. Using a simple single-layered structure, the proposed scheme results in convergence of the actual neural weights to the embedded ERP patterns. The method is applied to real event-related potential data recorded during a common odd-ball type paradigm. For the first time, within-session variable signal patterns are automatically identified, dismissing the strong and limiting requirement of a priori stimulus-related selective grouping of the recorded data. The results present new possibilities in ERP research.     

Noise reduction in rhythmic and multitrial biosignals with applications to event-related potentials

A new noise reduction algorithm is presented for signals displaying repeated patterns or multiple trials. Each pattern is stored in a matrix, forming a set of events, which is termed multievent signal. Each event is considered as an affine transform of a basic template signal that allows for time scaling and shifting. Wavelet transforms, decimated and undecimated, are applied to each event. Noise reduction on the set of coefficients of the transformed events is applied using either wavelet de- noising or principal component analysis (PCA) noise reduction methodologies. The method does not require any manual selection of coefficients. Nonstationary multievent synthetic signals are employed to demonstrate the performance of the method using normalized mean square error against classical wavelet and PCA based algorithms. The new method shows a significant improvement in low SNRs (typically <0 dB). On the experimental side, evoked potentials in a visual oddball paradigm are used. The reduced-noise visual oddball event-related potentials reveal gradual changes in morphology from trial to trial (especially for N1-P2 and N2-P3 waves at Fz), which can be hypothetically linked to attention or decision processes. The new noise reduction method is, thus, shown to be particularly suited for recovering single-event features in non- stationary low SNR multievent contexts.     

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.     

MSE behaviour of biomedical event-related filters [impedancecardiography application]

The mean-squared error (MSE) behaviour for Fourier linear combiner (FLC)-based filters is analyzed, using the independence assumption. The advantage of this analysis is its simplicity compared with previous results. The MSE transient behaviour for this kind of filters is also presented for the first time. Moreover, a time-varying sequence for the least mean square (LMS) algorithm step-size is proposed to provide fast convergence with small misadjustment error. It is shown that for this sequence, the MSE behaves better as the input signal-to-noise ratio (SNR) decreases, but increases with the number of harmonics. Lastly, the authors make a brief analysis on the nonstationary behaviour of these filters, and again they find simple expressions for the MSE behaviour     

A basis transformation technique with application to scattering by wires

A numerical basis transformation technique is described which may be applied, in conjunction with point-matching methods (e.g., piecewise uniform or piecewise linear methods), to obtain least-square solutions of electromagnetic scattering by thin wires. It is shown that reductions in both computer solution time and computer storage requirements result. The technique is demonstrated by applying it along with piecewise uniform methods to the solution of scattering by circular loops and straight wires.     

全自动尿流式分析在临床应用中的研究

尿流式分析仪与传统的显微镜检测相比，提高了计数的精确度和准确度并且节约了大量的实验室劳动，但是它缺少国际公认的参考范围，因此是应用中的主要缺陷，目前无离心尿体外活动染色用相差显微镜进行计数池计数被认为是最好的确认定参考值的方法。UF-100(日本东业医疗电子有限公司)用氩激光流式分析仪可确认红细胞、白细胞、上皮细胞、移行上皮、细菌、管型、精子、结晶等。对它的评价已经建立一个线性范围，但是不够精确，一致性和意义不如显微镜，UF-100与计数池计数，定量尿镜检、沉渣计数、干化学、细菌培养的对比是为了进行复查。临床应用包括尿路感染的诊断、血尿的来源定位和肾病的诊断、监控和排除。最有价值的方法是把干化和UF-100联合应用作为初步筛选方法的提出，减少镜检的重复性，节约了实验室劳动，扩大临床应用．     

Sequential Karhunen-Loeve basis extraction and its application toimages

The Karhunen-Loeve (KL) transform is an optimal method for approximating a set of vectors or images, which was used in image processing and computer vision for several tasks such as face and object recognition. Its computational demands and its batch calculation nature have limited its application. Here we present a new, sequential algorithm for calculating the KL basis, which is faster in typical applications and is especially advantageous for image sequences: the KL basis calculation is done with much lower delay and allows for dynamic updating of image databases. Systematic tests of the implemented algorithm show that these advantages are indeed obtained with the same accuracy available from batch KL algorithms.     

Multiresolution wavelet analysis of evoked potentials

Neurological injury, such as from cerebral hypoxia, appears to cause complex changes in the shape of evoked potential (EP) signals. To characterize such changes we analyze EP signals with the aid of scaling functions called wavelets. In particular, we consider multiresolution wavelets that are a family of orthonormal functions. In the time domain, the multiresolution wavelets analyze EP signals at coarse or successively greater levels of temporal detail. In the frequency domain, the multiresolution wavelets resolve the EP signal into independent spectral bands. In an experimental demonstration of the method, somatosensory EP signals recorded during cerebral hypoxia in anesthetized cats are analyzed. Results obtained by multiresolution wavelet analysis are compared with conventional time-domain analysis and Fourier series expansions of the same signals. Multiresolution wavelet analysis appears to be a different, sensitive way to analyze EP signal features and to follow the EP signal trends in neurologic injury. Two characteristics appear to be of diagnostic value: the detail component of the MRW displays an early and a more rapid decline in response to hypoxic injury while the coarse component displays an earlier recovery upon reoxygenation     

Analyzing functional brain connectivity by means of commute times: a new approach and its application to track event-related dynamics

There is growing interest in studying the association of functional connectivity patterns with particular cognitive tasks. The ability of graphs to encapsulate relational data has been exploited in many related studies, where functional networks (sketched by different neural synchrony estimators) are characterized by a rich repertoire of graph-related metrics. We introduce commute times (CTs) as an alternative way to capture the true interplay between the nodes of a functional connectivity graph (FCG). CT is a measure of the time taken for a random walk to setout and return between a pair of nodes on a graph. Its computation is considered here as a robust and accurate integration, over the FCG, of the individual pairwise measurements of functional coupling. To demonstrate the benefits from our approach, we attempted the characterization of time evolving connectivity patterns derived from EEG signals recorded while the subject was engaged in an eye-movement task. With respect to standard ways, which are currently employed to characterize connectivity, an improved detection of event-related dynamical changes is noticeable. CTs appear to be a promising technique for deriving temporal fingerprints of the brain's dynamic functional organization.     

Time-scale analysis of motor unit action potentials

Quantitative analysis in clinical electromyography (EMG) is very desirable because it allows a more standardized, sensitive and specific evaluation of the neurophysiological findings, especially for the assessment of neuromuscular disorders. Following the recent development of computer-aided EMG equipment, different methodologies in the time domain and frequency domain have been followed for quantitative analysis. In this study, the usefulness of the wavelet transform (WT), that provides a linear time-scale representation is investigated, for describing motor unit action potential (MUAP) morphology. The motivation behind the use of the WT is that it provides localized statistical measures (the scalogram) for nonstationary signal analysis. The following four WT's were investigated in analyzing a total of 800 MUAP's recorded from 12 normal subjects, 15 subjects suffering with motor neuron disease, and 13 from myopathy: Daubechies with four and 20 coefficients, Chui (CH), and Battle-Lemarie (BL). The results are summarized as follows: 1) most of the energy of the MUAP signal is distributed among a small number of well-localized (in time) WT coefficients in the region of the main spike, 2) for MUAP signals, we look to the low-frequency coefficients for capturing the average waveshape of the MUAP signal over long durations, and we look to the high-frequency coefficients for locating MUAP spike changes, 3) the Daubechies 4 wavelet, is effective in tracking the transient components of the MUAP signal, 4) the linear spline CH (semiorthogonal) wavelet provides the best MUAP signal approximation by capturing most of the energy in the lowest resolution approximation coefficients, and 5) neural network DY (DY) of Daubechies 4 and BL WT coefficients was in the region of 66%, whereas DY for the empirically determined time domain feature set was 78%. In conclusion, wavelet analysis provides a new way in describing MUAP morphology in the time-frequency plane. This method allows for the fast extraction of localized frequency components, which when combined with time domain analysis into a modular neural network decision support system enhances further the DY to 82.5% aiding the neurophysiologist in the early and accurate diagnosis of neuromuscular disorders.     

Maximum likelihood analysis of cardiac late potentials

This study presents a new time-domain method for the detection of late potentials in individual leads. Basic statistical properties of the ECG samples are modeled in order to estimate the amplitude and duration of late potentials. The signal model accounts for correlation in both time and across the ensemble of beats. Late potentials are modeled as a colored process with unknown amplitude which is disturbed by white, Gaussian noise. Maximum likelihood estimation is applied to the model for estimating the amplitude of the late potentials. The resulting estimator consists of an eigenvector-based filter followed by a nonlinear operation. The performance of the maximum likelihood procedure was compared to that obtained by traditional time-domain analysis based on the vector magnitude. It was found that the new technique yielded a substantial improvement of the signal-to-noise ratio in the function used for endpoint determination. This improvement leads to a prolongation of the filtered QRS duration in cases with late potentials     

Spectral analysis of motor unit action potentials

The statistical processing of electromyographic signal examination performed in the time domain ensures mostly correct classification of pathology; however, because of an ambiguity of most temporal parameter definitions, a diagnosis can include a significant error that strongly depends on the neurologist's experience. Then, selected temporal parameters are determined for each run, and their mean values are calculated. In the final stage, these mean values are compared with a standard and, including additional clinical information, a diagnosis is given. An inconvenience of this procedure is high time consumption that arises from the necessity of determination of many parameters. Additionally, an ambiguity in determination of basic temporal parameters can cause doubts when parameters found by the physician are compared with standard parameters determined in other research centers. In this paper, we present a definition for spectral discriminant that directly enables a unique diagnosis to be made. An essential advantage of the suggested discriminant is a precise and algorithmically realized definition that enables an objective comparison of examination results obtained by physicians with different experiences or working in different research centers. A suggestion of the standard for selected muscle based on a population of 70 healthy cases is presented in the Results section.