Automatic differentiation of multichannel EEG signals

Intention of movement of left or right index finger, or right foot is recognized in electroencephalograms (EEGs) from three subjects. We present a multichannel classification method that uses a "committee" of artificial neural networks to do this. The classification method automatically finds spatial regions on the skull relevant for the classification task. Depending on subject, correct recognition of intended movement was achieved in 75%-98% of trials not seen previously by the committee, on the basis of single EEGs of one-second duration. Frequency filtering did not improve recognition. Classification was optimal during the actual movement, but a first peak in the classification success rate was observed in all subjects already when they had been cued which movement later to perform.     

Time-frequency spectral estimation of multichannel EEG using the Auto-SLEX method

In this paper, we apply a new time-frequency spectral estimation method for multichannel data to epileptiform electroencephalography (EEG). The method is based on the smooth localized complex exponentials (SLEX) functions which are time-frequency localized versions of the Fourier functions and, hence, are ideal for analyzing nonstationary signals whose spectral properties evolve over time. The SLEX functions are simultaneously orthogonal and localized in time and frequency because they are obtained by applying a projection operator rather than a window or taper. In this paper, we present the Auto-SLEX method which is a statistical method that 1) computes the periodogram using the SLEX transform, 2) automatically segments the signal into approximately stationary segments using an objective criterion that is based on log energy, and 3) automatically selects the optimal bandwidth of the spectral smoothing window. The method is applied to the intracranial EEG from a patient with temporal lobe epilepsy. This analysis reveals a reduction in average duration of stationarity in preseizure epochs of data compared to baseline. These changes begin up to hours prior to electrical seizure onset in this patient.     

On nonexistence of the maximum likelihood estimate in blind multichannel identification

In this paper, a blind multichannel identification problem for which the maximum likelihood estimate (MLE) does not exist is considered. More specifically, the likelihood function associated with this problem turns out to have no maximum but only saddle points. This interesting instance of nonexistence of the MLE for a practically relevant problem was first presented in the statistical literature on errors-in-variables regression (M. Solari, 1969). New insights into this result are presented in this paper, along with a direct proof based on the indefiniteness of the Hessian matrix.     

Employing spatially constrained ICA and wavelet denoising, for automatic removal of artifacts from multichannel EEG data

Detecting artifacts produced in electroencephalographic (EEG) data by muscle activity, eye blinks and electrical noise, etc., is an important problem in EEG signal processing research. These artifacts must be corrected before further analysis because it renders subsequent analysis very error-prone. One solution is to reject the data segment if artifact is present during the observation interval, however, the rejected data segment could contain important information masked by the artifact. The independent component analysis (ICA) can be an effective and applicable method for EEG denoising. The goal of this paper is to propose a framework, based on ICA and wavelet denoising (WD), to improve the pre-processing of EEG signals. In particular we employ concept of the spatially constrained ICA (SCICA) to extract artifact-only independent components (ICs) from the given EEG data, use WD to remove any cerebral activity from the extracted-artifacts ICs, and finally project back the artifacts to be subtracted from EEG signals to get clean EEG data. The main advantage of the proposed approach is faster computation, as it is not necessary to identify all ICs. Computer experiments are carried out, which demonstrate effectiveness of the proposed approach in removing focal artifacts that can be well separated by SCICA.     

A matrix-based algorithm for estimating multiple coherence of a periodic signal and its application to the multichannel EEG during sensory stimulation

The coherence between the stimulation signal and the electroencephalogram (EEG) has been used in the detection of evoked responses. The detector's performance, however, depends on both the signal-to-noise ratio (SNR) of the responses and the number of data segments (M) used in coherence estimation. In practical situations, when a given SNR occurs, detection can only be improved by increasing M and hence the total data length. This is particularly relevant when monitoring is the objective. In the present study, we propose a matrix-based algorithm for estimating the multiple coherence of the stimulation signal taking into account a set of N EEG channels as a way of increasing the detection rate for a fixed value of M. Monte Carlo simulations suggest that thresholds for such multivariate detector are the same as those for multiple coherence of Gaussian signals and that using more than six signals is not advisable for improving the detection rate with M = 10. The results with EEG from 12 normal subjects during photic stimulation at 10 Hz showed a maximum detection for N greater than 2 in 58% of the subjects with M = 10, and hence suggest that the proposed multivariate detector is valuable in evoked responses applications.     

Mining reproducible activation patterns in epileptic intracerebral EEG signals: application to interictal activity

The study of interictal transient events may substantially complement the analysis of seizures in the presurgical evaluation of intractable epilepsy. A comprehensive methodology of quantifying reproducibility of activation patterns in intracerebral electroencephalography signals is presented. It may be applied to various forms of transient epileptic events under the assumption that a time of occurrence may be assigned to them. In this paper, the method is used on two different forms of interictal events (interictal spikes or sharpwaves and transient bursts of fast activity). The methodology is based on signal processing and data mining algorithms and proceeds in three steps: (1) detection of transient paroxysmal events (monochannel event); (2) identification of quasisynchronous transient paroxysmal events (multichannel events); and (3) automatic extraction of similar activation patterns. Results show that the methodology allows reproducible sequential activation sets to be identified from signals recorded in four patients. Potential advantages of the method are discussed with respect to other approaches.     

Theory of multichannel magnetic stimulation: toward functionalneuromuscular rehabilitation

Human excitable cells can be stimulated noninvasively with externally applied time-varying electromagnetic fields. The stimulation can be achieved either by directly driving current into the tissue (electrical stimulation) or by means of electro-magnetic induction (magnetic stimulation). While the electrical stimulation of the peripheral neuromuscular system has many beneficial applications, peripheral magnetic stimulation has so far only a few. This paper analyzes theoretically the use of multiple magnetic stimulation coils to better control the excitation and also to eventually mimic electrical stimulation. Multiple coils allow electronic spatial adjustment of the shape and location of the stimulus without moving the coils. The new properties may enable unforeseen uses for peripheral magnetic stimulation, e.g., in rehabilitation of patients with neuromuscular impairment.     

Automated analysis of the electrical activity of the human brain (EEG): A progress report

Clinical evaluation of electroencephalographic (EEG) recordings is based on complex subjective processes of data reduction and feature extraction. The high dimensionality of the EEG signal, its variability, and the lack of standard population values have retarded development of automated systems. An interactive, real-time analysis system (ADIEEG) has been implemented to develop features to simplify visual interpretation and facilitate automated classification. It uses a 40 000 word PDP15-PDP11 dual processor computer. Resident code occupies approximately 11 000 locations, while a maximum of 12 000 locations are used for buffers. The system performs 1) continuous spectral analysis using the fast Fourier transform to produce estimates of power and coherence, 2) parallel time domain analysis to detect sharp transients significant to diagnosis, 3) several forms of graphics, 4) simple algorithms to reject noncortical and instrumental artifact, 5) interactive parameter alteration and on-line feedback to adjust decision thresholds when necessary, and 6) extraction of diagnostically helpful features using heuristics based on clinical EEG. The ADIEEG system resides in the University of California, San Francisco Medical Center, and Langley Porter Neuropsychiatric Institute.     

Estimation of coherence between blood flow and spontaneous EEG activity in neonates

Blood flow to the brain responds to changes in neuronal activity and, thus, metabolic demand. In earlier work, we observed correlation between cerebral blood flow and spontaneous electroencephalogram (EEG) activity in neonates. Using coherence, we now found that during Tracé Alternant EEG activity in quiet sleep of normal term neonates, this correlation is strongest at frequencies around 0.1 Hz, reaching statistical significance (p < 0.05) in six of the nine subjects studied (p < 0.07 in eight subjects). Due to noise, artifact, and spontaneous changes in the subjects' EEG patterns, the signals investigated included epochs of missing samples. We, therefore, developed a novel algorithm for the estimation of coherence in such data and applied a Monte Carlo (surrogate data) method for its statistical analysis. This process provides a test for the statistical significance of the maximum coherence within a selected frequency band. In addition to permitting further insight into the mechanisms of cerebral blood flow control, these algorithms are potentially of great benefit in a wide range of biomedical applications, where interrupted (gapped) recordings are often a problem.     

Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss

Diffraction propagation over hills and ridges at VHF and UHF is commonly estimated using Fresnel knife edge diffraction. This approach has the advantage of simplicity, and for many geometries yields accurate results. However, since it neglects the shape and composition of the diffracting surface, it can in some cases yield results which are in serious disagreement with measurements. To remedy this, attempts have been made to approximate the diffracting hill or ridge by other shapes, most notably cylinders. These approaches have not been widely adopted, due in large part to their greater numerical complexity. In this paper it is proposed to apply wedge diffraction in the format of the geometrical theory of diffraction (GTD), modified to include finite conductivity and local surface roughness effects. It is shown that, for geometries with grazing incidence and/or diffraction angles, significant improvement in accuracy is obtained. Further, the GTD wedge diffraction form used is based on the Fresnel integral, so that it is only slightly more complex numerically than knife edge diffraction. Finally, the GTD includes reflections from the sides of the ridge (wedge faces), and can be extended to multiple ridge diffraction and three-dimensional terrain variations.     

Enhancement of deep epileptiform activity in the EEG via 3-Dadaptive spatial filtering

The detection of epileptiform discharges (ED's) in the electroencephalogram (EEG) is an important component in the diagnosis of epilepsy. However, when the epileptogenic source is located deep in the brain, the ED's at the scalp are often masked by more superficial, higher-amplitude EEG activity. A noninvasive technique which uses an adaptive "beamformer" spatial filter has been investigated for the enhancement of signals from deep sources in the brain suspected of containing ED's. A forward three-layer spherical model was used to relate a dipolar source to recorded signals to determine the beamformer's spatial response constraints. The beamformer adapts, using the least-mean-squares (LMS) algorithm, to reduce signals from sources distant to some arbitrarily defined location in the brain. The beamformer produces three outputs, being the orthogonal components of the signal estimated to have arisen at or near the assumed location. Simulations were performed by using the same forward model to superimpose realistic ED's on normal EEG recordings. The simulations show the beamformer's ability to enhance signals emanating from deep foci by way of an enhancement ratio (ER), being the improvement in signal-to-noise ratio (SNR) to that observed at any of the scalp electrodes. The performance of the beamformer has been evaluated for 1) the number of scalp electrodes, 2) the recording montage, 3) dependence on the background EEG, 4) dependence on magnitude, depth, and orientation of epileptogenic focus, and 5) sensitivity to inaccuracies in the estimated location of the focus. Results from the simulations show the beamformer's performance to be dependent on the number of electrodes and moderately sensitive to variations in the EEG background. Conversely, its performance appears to be largely independent of the amplitude and morphology of the ED. The dependence studies indicated that the beamformer's performance was moderately dependent on eccentricity with the ER increasing as the dipolar source and the beamformer were moved from the center to the surface of the brain (1.51-2.26 for radial dipoles and 1.17-2.69 for tangential dipoles). The beamformer was also moderately dependent on variations in polar or azimuthal angle for radial and tangential dipoles. Higher ER's tended to be seen for locations between electrode sites. The beamformer was more sensitive to inaccuracies in both polar and azimuthal location than depth of the dipolar source. For polar locations, an ER > 1.0 was achieved when the beamformer was located within +/- 25 degrees of a radial dipole and +/- 35 degrees of a tangential dipole. Similarly, angular ranges of +/- 37.5 degrees and +/- 45 degrees, respectively, for inaccuracies in azimuthal locations. Preliminary results from real EEG records, comprising 12 definite or questionable epileptiform events, from four patients, demonstrated the beamformer's ability to enhance these events by a mean 100% (52%-215%) for referential data and a mean 104% (50%-145%) for bipolar data.     

Localizing functional activity in the brain through time-frequencyanalysis and synthesis of the EEG

Multichannel electroencephalograms (EEGs) are processed using time-frequency (TF) analysis and synthesis techniques to geometrically localize neuroelectric generators of specific activity contained within the observed EEG. The TF domain techniques are utilized to separate the signals of interest from the remainder of the EEG, by allowing the definition of regions of interest which contain the signals for which we desire to localize the underlying neuronal generators. This approach essentially introduces a filtering technique which allows the distortionless separation of the signals of interest from all other components recorded. The source of the functional activity in the brain is estimated and mapped numerically by a least-squares approach. We have applied these techniques to identify the anatomical location of the sleep spindle, a component of the EEG observed during sleep, which is of importance in understanding the generation of sleep and sleep patterns     

Approximating dipoles from human EEG activity: the effect of dipolesource configuration on dipolarity using single dipole models

Dipolarity is the goodness-of-fit of the observed potential distribution with one calculated using specific assumptions about the source of the electrical potential distribution. The authors used computer simulations to examine the effect of different distributions of sources on their resulting dipolarity values. Electric dipoles were placed in a head-shaped model with uniform conductivity using four different dipole configurations (randomly oriented dipoles, a uniform dipole disk layer, a dipole disk layer with uniformly distributed holes, or one with randomly oriented dipoles). The best-fitting single dipole for each configuration was calculated and the dipolarity was computed as the mean squared error of the electrical potential distributions generated by the actual dipole configuration and by the best-fitting single dipole. The simulations show that: 1) a smooth dipole layer with or without holes gives dipolarities above 99.5% even when extended over areas as large as 1256 mm²; 2) randomly oriented dipoles under a smooth dipole layer also give dipolarities above 99.5%; and 3) randomly oriented and distributed dipoles, even if contained in a small portion of the total area, give dipolarities below 93.0%. These simulations show that inhomogeneity (holes) within a dipole disk layer per se do not lower dipolarity; rather, it is the random orientation and distribution of these dipoles which lowers dipolarity. Furthermore, dipolarity is not lowered by such randomly oriented and distributed dipoles when they are beneath a dipole disk layer     

The experimental demonstration of a multichannel time-seriesmyoprocessor: system testing and evaluation

A multichannel time-series myoprocessor which combines the advantages of the parallel filtering limb function classifiers of Doerschuk et al. and the "optimal myoprocessor" muscle force estimators described by Hogan et al. have been developed and evaluated experimentally. Magnitudes and directions of knee movements were identified accurately and robustly from EMG sites intermediate to the major thigh muscles of intact individuals. Electrode placement criteria were tested, and system performance and sensitivity to contraction level as functions of channel number were computed. By including spatially distributed information into the structure of the processor, gains in accuracy and reliability over systems with fewer channels were demonstrated. Operating range increased with the number of channels included in the processor. Joint moment was estimated from multiple channels of temporally correlated data, extending and generalizing previously reported techniques. Identifying the parameters of AR models of the EMG at low levels of contraction resulted in more robust classification and joint moment estimation. Optimal electrode position could not be predicted a priori. The system may be applicable to the proportional control of myoelectric prostheses.     

EVAM: an eigenvector-based algorithm for multichannel blinddeconvolution of input colored signals

A new algorithm is proposed for the deconvolution of an unknown, possibly colored, Gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions. More specifically, not only the root (pole and zero) locations but also the orders of the channel transfer functions are unknown. It is assumed that the channel orders may be overestimated. The proposed algorithm estimates the orders and root locations of the channel transfer functions, therefore it can also be used in multichannel system identification problems. The input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal, hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones. Several experimental results indicate improvement compared to the existing methods in the literature     

阵列波导光栅中自由传播区模式的有效折射率

针对阵列波导光栅设计中自由传播区模式有效折射率的确定问题,提出了一种采用加权等效模式折射率作为自由传播区模式有效折射率的方法。通过引入慢变包络近似条件并采用吸收边界条件的一阶Galerkin有限元法,给出了阵列波导光栅自由传播区仅含有磁场分量的全矢量波动方程组。在此基础上,基于三维全矢量束传播法对自由传播区光场进行了模式分析,并结合导模传输分析法,推导给出了加权等效模式折射率的表达式,为阵列波导光栅设计中自由传播区模式折射率的确定提供了一个理论依据。     

Comprehensive common spatial patterns with temporal structure information of EEG data: minimizing nontask related EEG component

In the context of electroencephalogram (EEG)-based brain-computer interfaces (BCI), common spatial patterns (CSP) is widely used for spatially filtering multichannel EEG signals. CSP is a supervised learning technique depending on only labeled trials. Its generalization performance deteriorates due to overfitting occurred when the number of training trials is small. On the other hand, a large number of unlabeled trials are relatively easy to obtain. In this paper, we contribute a comprehensive learning scheme of CSP (cCSP) that learns on both labeled and unlabeled trials. cCSP regularizes the objective function of CSP by preserving the temporal relationship among samples of unlabeled trials in terms of linear representation. The intrinsically temporal structure is characterized by an l(1) graph. As a result, the temporal correlation information of unlabeled trials is incorporated into CSP, yielding enhanced generalization capacity. Interestingly, the regularizer of cCSP can be interpreted as minimizing a nontask related EEG component, which helps cCSP alleviate nonstationarities. Experiment results of single-trial EEG classification on publicly available EEG datasets confirm the effectiveness of the proposed method.     

Adaptive multichannel data dissemination: support of dynamic traffic awareness and push-pull time balance

Data dissemination by the use of periodic broadcast is a viable scalable mechanism due to the explosion of information services in wireless networks. Many research works have exploited the data broadcast methodologies, however, upon the premise that the broadcast traffic is static on a single broadcast channel. In practice, the broadcast traffic changes dynamically and multiple broadcast channels can be utilized for efficient data dissemination. Accordingly, in this paper we devise an adaptive multichannel data-dissemination mechanism, including two components: the multichannel traffic-awareness and the deterministic balance search techniques. The multichannel traffic-awareness technique performs a cyclic estimation of dynamic access frequency distribution in response to traffic dynamics. With the measured estimation, the deterministic balance search technique adjusts channel allocation and item classification to further minimize and balance the push access and the pull response time. The experimental results show that the proposed mechanism is able to attain the result of channel partition and item classification very close to the optimum and, thus, minimize the mean access time in both push and pull channels simultaneously. Therefore, the reliability of broadcast contents is guaranteed.