A novel adaptive beamformer for MEG source reconstruction effective when large background brain activities exist

This paper proposes a novel prewhitening eigenspace beamformer suitable for magnetoencephalogram (MEG) source reconstruction when large background brain activities exist. The prerequisite for the method is that control-state measurements, which contain only the contributions from the background interference, be available, and that the covariance matrix of the background interference can be obtained from such control-state measurements. The proposed method then uses this interference covariance matrix to remove the influence of the interference in the reconstruction obtained from the target measurements. A numerical example, as well as applications to two types of MEG data, demonstrates the effectiveness of the proposed method.     

Blind Unitary Prewhitening with a Real-Valued Eigendecomposition

Prewhitening is a standard step for the processing of noisy signals. Typically, eigenvalue decomposition (EVD) of the sample data covariance matrix is used to calculate the whitening matrix. From a computational point of view, an important problem here is to reduce the complexity of the EVD of the complex-valued sample data covariance matrix. In this paper, we show that the computational complexity of the prewhitening step for complex-valued signals can be reduced approximately by a factor of four when the real-valued EVD is used instead of the complex-valued one. Such complexity reduction can be achieved for any axis-symmetric array. The performance of the proposed procedure is studied in application to a blind source separation (BSS) problem. For this application, the performance of the proposed prewhitening scheme is illustrated by means of simulations, and compared with the conventional prewhitening scheme. Among a number of BSS methods which use prewhitening, the second-order blind identification procedure has been adopted in this paper.     

A resampling method for estimating the signal subspace of spatio-temporal EEG/MEG data

Source localization using spatio-temporal electroencephalography (EEG) and magnetoencephalography (MEG) data is usually performed by means of signal subspace methods. The first step of these methods is the estimation of a set of vectors that spans a subspace containing as well as possible the signal of interest. This estimation is usually performed by means of a singular value decomposition (SVD) of the data matrix: The rank of the signal subspace (denoted by r) is estimated from a plot in which the singular values are plotted against their rank order, and the signal subspace itself is estimated by the first r singular vectors. The main problem with this method is that it is strongly affected by spatial covariance in the noise. Therefore, two methods are proposed that are much less affected by this spatial covariance, and old and a new method. The old method involves prewhitening of the data matrix, making use of an estimate of the spatial noise covariance matrix. The new method is based on the matrix product of two average data matrices, resulting from a random partition of a set of stochastically independent replications of the spatio-temporal data matrix. The estimated signal subspace is obtained by first filtering out the asymmetric and negative definite components of this matrix product and then retaining the eigenvectors that correspond to the r largest eigenvalues of this filtered data matrix. The main advantages of the partition-based eigen decomposition over prewhited SVD is that 1) it does not require an estimate of the spatial noise covariance matrix and 2b) that it allows one to make use of a resampling distribution (the so-called partitioning distribution) as a natural quantification of the uncertainty in the estimated rank. The performance of three methods (SVD with and without prewhitening, and the partition-based method) is compared in a simulation study. From this study, it could be concluded that prewhited SVD and the partition-based eigen decomposition perform equally well when the amplitude time series are constant, but that the partition-based method performs better when the amplitude time series are variable.     

基于fMRI功能网络和贝叶斯矩阵分解的脑电源成像方法

脑电(EEG)是一种重要的脑功能成像技术,根据头皮记录的EEG信号重构皮层脑活动称为EEG源成像。然而脑源活动位置和尺寸的准确重构依然是一个挑战。为充分利用EEG和功能磁共振(fMRI)信号在时空分辨率上的互补信息,该文提出一个新的源成像方法——基于fMRI脑网络和时空约束的EEG源重构算法(FN-STCSI)。该方法在参数贝叶斯框架下,基于矩阵分解思想将源信号分解为若干时间基函数的线性组合。此外,为融合fMRI的高空间分辨率信息,FN-STCSI利用独立成分分析提取fMRI信号的功能网络,构建EEG源成像的空间协方差基,通过变分贝叶斯推断技术确定每个空间协方差基的相对贡献,实现EEG-fMRI融合。通过蒙特卡罗数值仿真和实验数据分析比较了FN-STCSI与现有算法在不同信噪比和不同先验条件下的性能,结果表明FN-STCSI能有效融合EEG-fMRI在时空上的互补信息,提高EEG弥散源成像的性能。     

基于传播算子的卫星导航系统干扰源直接定位方法

针对现有单星定位技术精确度不足问题,提出一种基于传播算子的卫星导航系统干扰源直接定位方法,解决现有技术无法快速有效地定位中高轨卫星干扰源的问题。对卫星接收信号建模,计算每个时刻的接收信号协方差矩阵,通过对协方差矩阵分块,计算得到传播算子,进而得到导向矢量正交投影子空间的估计;然后建立损失函数,通过搜索得到干扰源位置估计结果。理论分析和仿真结果证明,该算法在复杂度大大降低的同时,定位精确度与传统基于多重信号分类(MUSIC)的直接定位算法相当,远优于现有的测向定位技术,具有重要的工程应用价值。     

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.     

Experimental results of localization of moving underwater signal byadaptive beamforming

The problem of weak moving signal localization and tracking in the presence of single motionless strong interference is investigated using real data of an underwater experiment in the Baltic sea (Sept. 1990) with a horizontal receiving array of 64 hydrophones and with two independent powerful narrowband sources imitating the signal and interference. Three simple adaptive beamforming methods were employed for the experimental data processing. The first one is based on the well-known projection approach to adaptive beamforming, the second method uses the adaptive canceler approach (also termed the dipole pattern method), and the third method combines these approaches. The signal-to-interference power ratio (SIR) threshold of the signal localization and tracking is evaluated by a special technique, which allows examination of the considered algorithms with change of the SIR in consecutive order. The results of the data processing show the high possibilities of signal localization in the presence of strong interference. The combined method performs better than the methods considered and enables localization of the signal source up to an SIR≃-25 dB     

Direction of Arrival Estimation in the Presence of Noise Coupling in Antenna Arrays

The direction of arrival (DOA) estimation problem in the presence of signal and noise coupling in antenna arrays is addressed. In many applications, such as smart antenna, radar and navigation systems, the noise coupling between different antenna array elements is often neglected in the antenna modeling and thus, may significantly degrade the system performance. Utilizing the exact noise covariance matrix enables to achieve high-performance source localization by taking into account the colored properties of the array noise. The noise covariance matrix of the antenna array consists of both the external noise sources from sky, ground and interference, and the internal noise sources from amplifiers and loads. Computation of the internal noise covariance matrix is implemented using the theory of noisy linear networks combined with the method of moments (MoM). Based on this noise statistical analysis, a new four-port antenna element consisting of two orthogonal loops is proposed with enhanced source localization performance. The maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) for DOA estimation in the presence of noise coupling is derived. Simulation results show that the noise coupling in antenna arrays may substantially alter the source localization performance. The performance of a mismatched ML estimator based on a model which ignores the noise coupling shows significant performance degradation due to noise coupling. These results demonstrate the importance of the noise coupling modeling in the DOA estimation algorithms.     

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.     

Sparse recovery method for far-field and near-field sources localization using oblique projection

In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.     

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.     

The Influence of Model Parameters on BEG/MEG Single Dipole Source Estimation

This paper deals with source localization and strength estimation based on EEG and MEG data. It describes an estimation method (inverse procedure) which uses a four-spheres model of the head and a single current dipole. The dependency of the inverse solution on model parameters is investigated. It is found that sphere radii and conductivities influence especially the strength of the EEG equivalent dipole and not its location or direction. The influence on the equivalent dipole of the gradiometer is investigated. In general the MEG produces better location estimates than the EEG whereas the reverse is found for the component estimates. An inverse solution simultaneously based on EEG and MEG data appears slightly better than the average of separate EEG and MEG solutions. Variances of parameter estimators which can be calculated on the basis of a linear approximation of the model, were tested by Monte Carlo simulations.     

Interference rejection in FFH systems using least squaresestimation techniques

A fast frequency-hopped (FFH) receiver which uses a prewhitening filter to reject narrowband interference is described. By using an appropriate fractional tap spacing, it is shown that interference can be estimated independently of the desired signal. Bit error rate results are presented for the receiver for linear square-law combining. The results compare favorably to those obtained by a near-optimal automatic gain-control (AGC) combining technique. The performance of the prewhitening filter interference rejection method is shown to be superior to that of a nonparametric self-normalizing receiver. Finally, simulation results for an FFH receiver using the complex least mean-square (LMS) algorithm to update the prewhitening filter coefficients are presented     

Brain source localization using reduced EEG sensors

Brain source activation is caused due to certain mental or physical task, and such activation is localized by using various optimization techniques. This localization has vital application for diagnoses of various brain disorders such as epilepsy, schizophrenia, Alzheimer, depression, Parkinson and stress. Various neuroimaging techniques (such as EEG, fMRI, MEG) are used to record brain activity for inference and estimation of active source locations. EEG employs set of sensors which are placed on scalp to measure electric potentials. These sensors have significant role in overall system complexity, computational time and system cost. Hence, sensor reduction for EEG source localization has been a topic of interest for researchers to develop a system with improved localization precision, less system complexity and reduced cost. This research work discusses and implements the brain source localization for real-time and synthetically generated EEG dataset with reduced number of sensors. For this, various optimization algorithms are used which include Bayesian framework-based multiple sparse priors (MSP), classical low-resolution brain electromagnetic tomography (LORETA), beamformer and minimum norm estimation (MNE). The results obtained are then compared in terms of negative variational free energy, localization error and computational time measured in seconds. It is observed that multiple sparse priors (MSP) with increased number of patches performed best even with reduced number of sensors, i.e., 7 instead of 74. The results are shown valid for synthetic EEG data at low SNR level, i.e., 5 dB and real-time EEG data, respectively.     

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.     

Evaluating the Performance of Kalman-Filter-Based EEG Source Localization

Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural framework for incorporating dynamic EEG generation models in source localization. Here, a recently developed inverse solution is introduced, which uses spatiotemporal Kalman filtering tuned through likelihood maximization. Standard diagnostic tests for objectively evaluating Kalman filter performance are then described and applied to inverse solutions for simulated and clinical EEG data. These tests, employed for the first time in Kalman-filter-based source localization, check the statistical properties of the innovation and validate the use of likelihood maximization for filter tuning. However, this analysis also reveals that the filter's existing space- and time-invariant process model, which contains a single fixed-frequency resonance, is unable to completely model the complex spatiotemporal dynamics of EEG data. This finding indicates that the algorithm could be improved by allowing the process model parameters to vary in space.      

Estimating stationary dipoles from MEG/EEG data contaminated withspatially and temporally correlated background noise

The stationary dipole model for the inverse problem of magnetoencephalographic (MEG) and electroencephalographic (EEG) data is extended by including spatio-temporal correlations of the background noise. For that purpose, the spatio-temporal covariances are described as a Kronkecker product of a spatial and a temporal covariance matrix. The maximum likelihood method is used to estimate this Kronecker product from a series of trials of MEG/EEG data. A simulation study shows that the inclusion of the background noise generally improves the dipole estimate substantially. When the frequency of the source time functions, however, coincides with the frequency contents of the covariance function, the dipole estimate worsens when the temporal correlations are included. The inclusion of spatial correlations always improves the estimates     

基于二阶锥规划的相干信号深零陷自适应波束形成

针对常规自适应波束形成算法在强相干干扰情况下零陷深度不够、甚至干扰抑制失效的问题,提出了一种基于二阶锥规划的相干信号深零陷自适应波束形成算法。该算法首先对接收数据协方差矩阵进行Toeplitz重构,使其包含信号和干扰的所有方位信息。然后重构了干扰加噪声协方差矩阵。接着在保证期望方向波束无失真前提下,约束主瓣宽度和旁瓣电平,使得波束形成器干扰和噪声的输出功率最小。最后将该问题转化为凸优化中的二阶锥规划问题,并使用凸优化工具箱进行快速求解。仿真结果验证了该算法的有效性。     

基于协方差矩阵重构和导向矢量估计的稳健自适应波束形成

实际应用中, 当假定的与真实的期望信号导向矢量之间存在一定误差时, 波束形成器的性能会急剧下降, 特别是当期望信号功率很强的时候.为解决这个问题, 提出了一种新的算法.当信源数小于阵元数时, 干扰加噪声协方差矩阵具有稀疏性.新方法首先利用该特性重构干扰加噪声协方差矩阵并由此得到与干扰导向矢量正交的子空间, 使接收的数据通过该子空间得到只含有期望信号和噪声的混合信号, 然后,对该混合信号基于最大化输出功率原理估计期望信号导向矢量, 最后,把得到的导向矢量和正交子空间来构造阵列加权值.仿真结果表明:该算法分别在假定的期望信号导向矢量存在误差、期望信号很强和低快拍数时仍然具有良好的性能.     

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