Estimation of number of independent brain electric sources from the scalp EEGs

In electromagnetic source analysis, many source localization strategies require the number of sources as an input parameter (e.g., spatio-temporal dipole fitting and the multiple signal classification). In the present study, an information criterion method, in which the penalty functions are selected based on the spatio-temporal source model, has been developed to estimate the number of independent dipole sources from electromagnetic measurements such as the electroencephalogram (EEG). Computer simulations were conducted to evaluate the effects of various parameters on the estimation of the source number. A three-concentric-spheres head model was used to approximate the head volume conductor. Three kinds of typical signal sources, i.e., the damped sinusoid sources, sinusoid sources with one frequency band and sinusoid sources with two separated frequency bands, were used to simulate the oscillation characteristics of brain electric sources. The simulation results suggest that the present method can provide a good estimate of the number of independent dipole sources from the EEG measurements. In addition, the present simulation results suggest that choosing the optimal penalty function can successfully reduce the effect of noise on the estimation of number of independent sources. The present study suggests that the information criterion method may provide a useful means in estimating the number of independent brain electrical sources from EEG/MEG measurements.     

基于变换数据空间的相干脑电源定位算法

不同脑区之间的相互协作对大脑完成认知任务具有重要意义.脑区电活动的相干性被认为是这种协作的表现形式.从头表脑电无创地三维定位相干源有助于了解大脑的内在机制.传统的MUSIC算法不能定位相干源.本文发展了一种在变换数据空间的MUSIC算法用于相干源定位.首先根据先验信息大致估计相干源区的范围,然后设计能压制相干源区的数据变换矩阵.最后在变换后的数据空间定位相干源.不同条件下的计算模拟实验表明,相比其它方法,这种方法具有更高的定位精度,运算速度也更快.     

Spatio-temporal EEG source localization using a three-dimensional subspace FINE approach in a realistic geometry inhomogeneous head model

The subspace source localization approach, i.e., first principle vectors (FINE), is able to enhance the spatial resolvability and localization accuracy for closely-spaced neural sources from EEG and MEG measurements. Computer simulations were conducted to evaluate the performance of the FINE algorithm in an inhomogeneous realistic geometry head model under a variety of conditions. The source localization abilities of FINE were examined at different cortical regions and at different depths. The present computer simulation results indicate that FINE has enhanced source localization capability, as compared with MUSIC and RAP-MUSIC, when sources are closely spaced, highly noise-contaminated, or inter-correlated. The source localization accuracy of FINE is better, for closely-spaced sources, than MUSIC at various noise levels, i.e., signal-to-noise ratio (SNR) from 6 dB to 16 dB, and RAP-MUSIC at relatively low noise levels, i.e., 6 dB to 12 dB. The FINE approach has been further applied to localize brain sources of motor potentials, obtained during the finger tapping tasks in a human subject. The experimental results suggest that the detailed neural activity distribution could be revealed by FINE. The present study suggests that FINE provides enhanced performance in localizing multiple closely spaced, and inter-correlated sources under low SNR, and may become an important alternative to brain source localization from EEG or MEG.     

A Bayesian approach to introducing anatomo-functional priors in theEEG/MEG inverse problem

We present a new approach to the recovering of dipole magnitudes in a distributed source model for magnetoencephalographic (MEG) and electroencephalographic (EEG) imaging. This method consists in introducing spatial and temporal a priori information as a cure to this ill-posed inverse problem. A nonlinear spatial regularization scheme allows the preservation of dipole moment discontinuities between some a priori noncorrelated sources, for instance, when considering dipoles located on both sides of a sulcus. Moreover, we introduce temporal smoothness constraints on dipole magnitude evolution at time scales smaller than those of cognitive processes. These priors are easily integrated into a Bayesian formalism, yielding a maximum a posteriori (MAP) estimator of brain electrical activity. Results from EEG simulations of our method are presented and compared with those of classical quadratic regularization and a now popular generalized minimum-norm technique called low-resolution electromagnetic tomography (LORETA)     

Three-Dimensional Imaging of Complex Neural Activation in Humans From EEG

Electro- or magnetoencephalography (EEG/MEG) are of utmost advantage in studying transient neuronal activity and its timing with respect to behavior in the working human brain. Direct localization of the neural substrates underlying EEG/MEG is commonly achieved by modeling neuronal activity as dipoles. However, the success of neural source localization with the dipole model has only been demonstrated in relatively simple localization tasks owing to the simplified model and its insufficiency in differentiating cortical sources with different extents. It would be of great interest to image complex neural activation with multiple sources of different cortical extensions directly from EEG/MEG. We have investigated this crucial issue by adding additional parameters to the dipole model, leading to the multipole model to better represent the extended sources confined to the convoluted cortical surface. The localization of multiple cortical sources is achieved by using the subspace source localization method with the multipole model. Its performance is evaluated with simulated data as compared with the dipole model, and further illustrated with the real data obtained during visual stimulations in human subjects. The interpretation of the localization results is fully supported by our knowledge about their anatomic locations and functional magnetic resonance imaging data in the same experimental setting. Methods for estimating multiple neuronal sources at cortical areas will facilitate our ability to characterize the cortical electrical activity from simple, early sensory components to more complex networks, such as in visual, motor, and cognitive tasks.     

Combined MEG and EEG source imaging by minimization of mutual information

Though very frequently assumed, the necessity to operate a joint processing of simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) recordings for functional brain imaging has never been clearly demonstrated. However, the very last generation of MEG instruments allows the simultaneous recording of brain magnetic fields and electrical potentials on the scalp. But the general fear regarding the fusion between MEG and EEG data is that the drawbacks from one modality will systematically spoil the performances of the other one without any consequent improvement. This is the case for instance for the estimation of deeper or radial sources with MEG. In this paper, we propose a method for a cooperative processing of MEG and EEG in a distributed source model. First, the evaluation of the respective performances of each modality for the estimation of every dipole in the source pattern is made using a conditional entropy criterion. Then, the algorithm operates a preprocessing of the MEG and EEG gain matrices which minimizes the mutual information between these two transfer functions, by a selective weighting of the MEG and EEG lead fields. This new combined EEG/MEG modality brings major improvements to the localization of active sources, together with reduced sensitivity to perturbations on data.     

Electromagnetic brain mapping

There has been tremendous advances in our ability to produce images of human brain function. Applications of functional brain imaging extend from improving our understanding of the basic mechanisms of cognitive processes to better characterization of pathologies that impair normal function. Magnetoencephalography (MEG) and electroencephalography (EEG) (MEG/EEG) localize neural electrical activity using noninvasive measurements of external electromagnetic signals. Among the available functional imaging techniques, MEG and EEG uniquely have temporal resolutions below 100 ms. This temporal precision allows us to explore the timing of basic neural processes at the level of cell assemblies. MEG/EEG source localization draws on a wide range of signal processing techniques including digital filtering, three-dimensional image analysis, array signal processing, image modeling and reconstruction, and, blind source separation and phase synchrony estimation. We describe the underlying models currently used in MEG/EEG source estimation and describe the various signal processing steps required to compute these sources. In particular we describe methods for computing the forward fields for known source distributions and parametric and imaging-based approaches to the inverse problem     

Recent Developments in Spatio-Temporal EEG Source Reconstruction Techniques

EEG is gaining recognition in the field of real-time applications. However, the EEG inverse problem leads to poor spatial resolution in brain source localization. This paper presents an overview of the existing EEG inverse solution methods. Further, a comparative analysis of recent techniques has been presented. This work discusses the challenges associated with the existing source reconstruction algorithms. The main focus is on the recent reports in this field that have combined the EEG denoising in the pre-processing phase along with the inverse localization approaches. Out of various existing techniques, SLORETA offers better localization results but its noise sensitivity is very high. It has been validated in a comparative analysis for simulated dipole sources with no noise. To illustrate the advantage of using pre-processed data with inverse localization, the classification accuracy of conventional methods has been compared. The accuracy has been analyzed for depression signals using the Naïve Bayes, RF, and SVM classifiers. The VMD- SLORETA method shows better accuracy as compared to EMD-SLORETA and SLORETA only. The existing EEG localization methods are efficient but the spatial resolution is still to be improved in the presence of various noise sources in raw EEG. More accurate localization is achieved by implementing denoising in combination with the source localization framework. There is a need to investigate further stages of EEG signal processing along with optimal feature selection. Further, additional studies should be conducted to improve the noise sensitivity of other existing localization systems using pre-processing approaches.

Graphic Abstract

     

Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE) Using a Hierarchical Bayesian Approach

We present an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model representation is motivated by the many random contributions to the path from sources to measurements including the tissue conductivity distribution, the geometry of the cortical surface, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE approach by comparison with source reconstruction methods that use fixed forward models. Analysis of simulated and real EEG data provide evidence that reconstruction of the forward model leads to improved source estimates.     

Estimation of neural dynamics from MEG/EEG cortical current density maps: application to the reconstruction of large-scale cortical synchrony

There is a growing interest in elucidating the role of specific patterns of neural dynamics--such as transient synchronization between distant cell assemblies--in brain functions. Magnetoencephalography (MEG)/electroencephalography (EEG) recordings consist in the spatial integration of the activity from large and multiple remotely located populations of neurons. Massive diffusive effects and poor signal-to-noise ratio (SNR) preclude the proper estimation of indices related to cortical dynamics from nonaveraged MEG/EEG surface recordings. Source localization from MEG/EEG surface recordings with its excellent time resolution could contribute to a better understanding of the working brain. We propose a robust and original approach to the MEG/EEG distributed inverse problem to better estimate neural dynamics of cortical sources. For this, the surrogate data method is introduced in the MEG/EEG inverse problem framework. We apply this approach on nonaveraged data with poor SNR using the minimum norm estimator and find source localization results weakly sensitive to noise. Surrogates allow the reduction of the source space in order to reconstruct MEG/EEG data with reduced biases in both source localization and time-series dynamics. Monte Carlo simulations and results obtained from real MEG data indicate it is possible to estimate non invasively an important part of cortical source locations and dynamic and, therefore, to reveal brain functional networks.     

Multi-way space-time-wave-vector analysis for EEG source separation

For the source analysis of electroencephalographic (EEG) data, both equivalent dipole models and more realistic distributed source models are employed. Several authors have shown that the canonical polyadic decomposition (also called ParaFac) of space-time-frequency (STF) data can be used to fit equivalent dipoles to the electric potential data. In this paper we propose a new multi-way approach based on space-time-wave-vector (STWV) data obtained by a 3D local Fourier transform over space accomplished on the measured data. This method can be seen as a preprocessing step that separates the sources, reduces noise as well as interference and extracts the source time signals. The results can further be used to localize either equivalent dipoles or distributed sources increasing the performance of conventional source localization techniques like, for example, LORETA. Moreover, we propose a new, iterative source localization algorithm, called Binary Coefficient Matching Pursuit (BCMP), which is based on a realistic distributed source model. Computer simulations are used to examine the performance of the STWV analysis in comparison to the STF technique for equivalent dipole fitting and to evaluate the efficiency of the STWV approach in combination with LORETA and BCMP, which leads to better results in case of the considered distributed source scenarios.     

Efficient dipole parameter estimation in EEG systems with near-ML performance

Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.     

Partially Constrained Blind Source Separation for Localization of Unknown Sources Exploiting Non-homogeneity of the Head Tissues

A new brain source localization technique using electroencephalograms (EEGs) is investigated in this paper. The information which describes the location of certain known sources is used as the constraint within the proposed blind source separation (BSS) algorithm and leads to a solution to the ill-posed inverse problem of source localization. Non-homogeneity of the head tissues, on the other hand, is exploited by introducing a realistic model of the mixing system. This model is used to better identify the location of the unknown sources within the brain from projection of the separated independent components on to the scalp. A separate procedure is employed to highlight the rhythmic EEG sources such as Alpha rhythm as the known sources. The performance of the scheme is shown on real EEG measurements and compared with that of “conventional dipole fitting algorithm”.

Projection versus prewhitening for EEG interference suppression

Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of the covariance of the interference plus noise. This approach is based on strong assumptions regarding temporal stationarity of the data, which do not commonly hold in EEG applications. In addition, prewhitening cannot typically be implemented directly due to ill conditioning of the covariance matrix, and ad hoc regularization is often necessary. Using both simulation examples and experiments involving real EEG data with auditory evoked responses, we demonstrate that a straightforward interference projection method is significantly more robust than prewhitening for EEG source localization.     

A novel phase congruency based algorithm for online data reduction in ambulatory EEG systems

Real signals are often corrupted by noise with a power spectrum variable over time. In applications involving these signals, it is expected that dynamically estimating and correcting for this noise would increase the amount of useful information extracted from the signal. One such application is scalp EEG monitoring in epilepsy, where electrical activity generated by cranio-facial muscles obscure the measured brainwaves. This paper presents a data-selection algorithm based on phase congruency to identify interictal spikes from background EEG; together with a novel statistical method that allows a more comprehensive trade-off based quantitative comparison of two algorithms which have been tested at a fixed threshold in the same database. Here, traditional phase congruency has been modified to incorporate a dynamic estimate of muscle activity present in the input scalp EEG signal. The proposed algorithm achieves 50% data reduction whilst detecting more than 80% of interictal spikes. This represents a significant improvement over the state-of-the-art denoising method for phase congruency.     

A Markov model for blind image separation by a mean-field EM algorithm.

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.     

基于组合阵列的水下特征线谱近场定位方法

本文提出了一种基于组合阵列的特征线谱定位方法,该方法仅采用均匀声压阵中心配置单只三维矢量水听器的基阵形式,即可完成近场源方位角、俯仰角和距离的三维参数估计,可为近场聚焦以及近场声全息等噪声源定位识别方法提供可靠的先验知识.该方法利用声源的二阶统计量信息,将三维参数估计问题转化为多个一维搜索问题,从而减少了算法的计算量,...     

Effects of head shape on EEGs and MEGs

This paper presents results of computer modeling studies of the effects of head shape on electroencephalograms (EEG's) and magnetoencephalograms (MEG's) and on the localization of electrical sources in the brain using these measurements. The effects of general, nonspherical head shape on EEG's and MEG's are determined by comparisons of EEG and MEG maps from nonspherical head models with corresponding maps from a spherical head model. The effects on source localization accuracy are determined by calculating moving dipole inverse solutions in a spherical head model using EEG's and MEG's from the nonspherical models and comparing the solutions with the known sources. It was found that nonspherical head shape can produce significant changes in the maps produced by some sources in the cortical region of the brain. However, it was also found that such deviations of the head from sphericity produce localization errors of less than approximately 1 cm. No significant differences in the effects of such deviations on EEG's and MEG's were found. Finally, it was found that most such deviations do not cause a dipolar source which is perpendicular to the surface of the head model to produce a significant magnetic field; such a source produces zero magnetic field in a sphere.     

Efficiency Evaluation of the Unconditional Maximum Likelihood Estimator for Near‐Field DOA Estimation

In this paper, we address the problem of closely spaced source localization using sensor array processing. In particular, the performance efficiency (measured in terms of the root mean square error) of the unconditional maximum likelihood (UML) algorithm for estimating the direction of arrival (DOA) of near‐field sources is evaluated. Four parameters are considered in this evaluation: angular separation among sources, signal‐to‐noise ratio (SNR), number of snapshots, and number of sources (multiple sources). Simulations are conducted to illustrate the UML performance to compute the DOA of sources in the near‐field. Finally, results are also presented that compare the performance of the UML DOA estimator with the existing multiple signal classification approach. The results show the capability of the UML estimator for estimating the DOA when the angular separation is taken into account as a critical parameter. These results are consistent in both low SNR and multiple‐source scenarios.