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.     

Joint azimuth, elevation, and time of arrival estimation of diffuse sources

In this paper, we estimate the azimuth, the elevation, and the time of arrival of diffuse sources using the covariance matching estimator (COMET) algorithm. Previous works dealt with azimuth estimation of diffuse sources or azimuth and time of arrival estimation of point sources. However, in realistic situations, a tridimensional diffuse source localization is needed, which is the main objective of this paper. We show that the dimensionality of the COMET algorithm can be reduced by separating the estimation of the different source powers and the noise variance from that of the remaining parameters, namely the azimuth, the elevation, the time of arrival, and the corresponding angular and temporal spreads. As COMET still involves a multidimensional nonlinear optimization, we choose, in this purpose, the alternating projection algorithm to alleviate the corresponding complexity. The multiple signal classification (MUSIC) algorithm is processed to initialize the so-resulted algorithm. Simulations of the proposed algorithm are carried in different contexts and compared to the Cramér-Rao Bound, MUSIC algorithm, and dispersed signal parametric estimation simulation results.     

Modified beamformers for coherent source region suppression

Many tomographic source localization algorithms used in biomagnetic imaging assume, explicitly or sometimes implicitly, that the source activity at different brain locations are either independent or that the correlation structure between sources is known. Among these algorithms is a class of adaptive spatial filters known as beamformers, which have superior spatiotemporal resolution abilities. The performance of beamformers is robust to weakly coherent sources. However, these algorithms are extremely sensitive to the presence of strongly coherent sources. A frequent mode of failure in beamformers occurs with reconstruction of auditory evoked fields (AEFs), in which bilateral auditory cortices are highly coherent in their activation. Here, we present a novel beamformer that suppresses activation from regions with interfering coherent sources. First, a volume containing the interfering sources is defined. The lead field matrix for this volume is computed and reduced into a few significant columns using singular value decomposition (SVD). A vector beamformer is then constructed by rejecting the contribution of sources in the suppression region while allowing for source reconstruction at other specified regions. Performance of this algorithm was first validated with simulated data. Subsequent tests of this modified beamformer were performed on bilateral AEF data. An unmodified vector beamformer using whole head coverage misplaces the source medially. After defining a suppression region containing the temporal cortex on one side, the described method consistently results in clear focal activations at expected regions of the contralateral superior temporal plane.     

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.     

Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks

A maximum likelihood (ML) acoustic source location estimation method is presented for the application in a wireless ad hoc sensor network. This method uses acoustic signal energy measurements taken at individual sensors of an ad hoc wireless sensor network to estimate the locations of multiple acoustic sources. Compared to the existing acoustic energy based source localization methods, this proposed ML method delivers more accurate results and offers the enhanced capability of multiple source localization. A multiresolution search algorithm and an expectation-maximization (EM) like iterative algorithm are proposed to expedite the computation of source locations. The Crame/spl acute/r-Rao Bound (CRB) of the ML source location estimate has been derived. The CRB is used to analyze the impacts of sensor placement to the accuracy of location estimates for single target scenario. Extensive simulations have been conducted. It is observed that the proposed ML method consistently outperforms existing acoustic energy based source localization methods. An example applying this method to track military vehicles using real world experiment data also demonstrates the performance advantage of this proposed method over a previously proposed acoustic energy source localization method.     

Recursive MUSIC: A framework for EEG and MEG source localization

The multiple signal classification (MUSIC) algorithm can be used to locate multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetocncephalography (MEG) data. The algorithm scans a single-dipole model through a three-dimensional (3-D) head volume and computes projections onto an estimated signal subspace. To locate the sources, the user must search the head volume for multiple local peaks in the projection metric. This task is time consuming and subjective. Here, the authors describe an extension of this approach which they refer to as recursive MUSIC (R-MUSIC). This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections. The new method is also able to locate synchronous sources through the use of a spatio-temporal independent topographies (IT) model. This model defines a source as one or more nonrotating dipoles with a single time course. Within this framework, the authors are able to locate fixed, rotating, and synchronous dipoles. The recursive subspace projection procedure that they introduce here uses the metric of canonical or subspace correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace, by recursively computing subspace correlations, the authors build up a model for the sources which account for a given set of data. They demonstrate here how R-MUSIC can easily extract multiple asynchronous dipolar sources that are difficult to find using the original MUSIC scan. The authors then demonstrate R-MUSIC applied to the more general IT model and show results for combinations of fixed, rotating, and synchronous dipoles     

An exact maximum likelihood registration algorithm for data fusion

Data fusion is a process dealing with the association, correlation, and combination of data and information from multiple sources to achieve refined position and identity estimates. We consider the registration problem, which is a prerequisite process of a data fusion system to accurately estimate and correct systematic errors. An exact maximum likelihood (EML) algorithm for registration is presented. The algorithm is implemented using a recursive two-step optimization that involves a modified Gauss-Newton procedure to ensure fast convergence. Statistical performance of the algorithm is also investigated, including its consistency and efficiency discussions. In particular, the explicit formulas for both the asymptotic covariance and the Cramer-Rao bound (CRB) are derived. Finally, simulated and real-life multiple radar data are used to evaluate the performance of the proposed algorithm     

基于频域单源区间的具有延迟的欠定盲分离

本文研究如何分离具有延迟而无回波的混叠信号.提出了欠定情况(即感知器少于源信号)下具有时间延迟的信道估计算法,称为单源区间衰减和延迟恢复(AD-MRISSI)算法;它在理论上能无偏差地估计信道,在应用中能准确地估计延迟和精确地估计衰减.也提出了一个基于稀疏原则的源信号重建算法,能避免Bofill算法中的求解二阶锥规划问题.几个语音信号实验展示了其有效性和实用性.     

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.      

有色过程噪声下的轮式机器人同步定位与地图构建

 由于机械制造工艺的原因,轮式机器人内部传感器获得的控制量在实际中为有色噪声,经典的同步定位与地图构建(SLAM)算法将不适用．提出一种有色过程噪声的机器人同步定位与地图构建算法．将机器人非线性过程模型线性化,用增广状态变量维数的方法将有色过程噪声模型转化为高斯白噪声模型．算法按照预测、观测、数据关联、更新、地图构建递推进行同步定位与地图构建．仿真结果表明,在有色过程噪声条件下,与EKF-SLAM算法和Fast-SLAM算法相比,提出的算法的机器人定位精度更好．     

Influence of head tissue conductivity in forward and inverse magnetoencephalographic simulations using realistic head models

The influence of head tissue conductivity on magnetoencephalography (MEG) was investigated by comparing the normal component of the magnetic field calculated at 61 detectors and the localization accuracy of realistic head finite element method (FEM) models using dipolar sources and containing altered scalp, skull, cerebrospinal fluid, gray, and white matter conductivities to the results obtained using a FEM realistic head model with the same dipolar sources but containing published baseline conductivity values. In the models containing altered conductivity values, the tissue conductivity values were varied, one at a time, between 10% and 200% of their baseline values, and then varied simultaneously. Although changes in conductivity values for a single tissue layer often altered the calculated magnetic field and source localization accuracy only slightly, varying multiple conductivity layers simultaneously caused significant discrepancies in calculated results. The conductivity of scalp, and to a lesser extent that of white and gray matter, appears especially influential in determining the magnetic field. Comparing the results obtained from models containing the baseline conductivity values to the results obtained using other published conductivity values suggests that inaccuracies can occur depending upon which tissue conductivity values are employed. We show the importance of accurate head tissue conductivities for MEG source localization in human brain, especially for deep dipole sources or when an accuracy greater than 1.4 cm is needed.     

Fractional delay estimation for blind source separation and localization of temporomandibular joint sounds

Temporomandibular joint (TMJ) sound sources are generated from the two joints connecting the lower jaw to the temporal bone. Such sounds are important diagnostic signs in patients suffering from temporomandibular disorder (TMD). In this study, we address the problem of source separation of the TMJ sounds. In particular, we examine patients with only one TMJ generating "clicks". Thereafter, we consider the TMJ sounds recorded from the two auditory canals as mixtures of clicks from the TMD joint and the noise produced by the other healthy/normal TMJ. We next exploit the statistical nonstationary nature of the TMJ signals by employing the degenerate unmixing estimation technique (DUET) algorithm, a time-frequency (T-F) approach to separate the sources. As the DUET algorithm requires the sensors to be closely spaced, which is not satisfied by our recording setup, we have to estimate the delay between the recorded TMJ sounds to perform an alignment of the mixtures. Thus, the proposed extension of DUET enables an essentially arbitrary separation of the sensors. It is also shown that DUET outperforms the convolutive Infomax algorithm in this particular TMJ source separation scenario. The spectra of both separated TMJ sources with our method are comparable to those available in existing literature. Examination of both spectra suggests that the click source has a better audible prominence than the healthy TMJ source. Furthermore, we address the problem of source localization. This can be achieved automatically by detecting the sign of our proposed mutual information estimator which exhibits a maximum at the delay between the two mixtures. As a result, the localized separated TMJ sources can be of great clinical value to dental specialists.     

A recursive algorithm for the three-dimensional imaging of brain electric activity: Shrinking LORETA-FOCUSS

Estimation of intracranial electric activity from the scalp electroencephalogram (EEG) requires a solution to the EEG inverse problem, which is known as an ill-conditioned problem. In order to yield a unique solution, weighted minimum norm least square (MNLS) inverse methods are generally used. This paper proposes a recursive algorithm, termed Shrinking LORETA-FOCUSS, which combines and expands upon the central features of two well-known weighted MNLS methods: LORETA and FOCUSS. This recursive algorithm makes iterative adjustments to the solution space as well as the weighting matrix, thereby dramatically reducing the computation load, and increasing local source resolution. Simulations are conducted on a 3-shell spherical head model registered to the Talairach human brain atlas. A comparative study of four different inverse methods, standard Weighted Minimum Norm, L1-norm, LORETA-FOCUSS and Shrinking LORETA-FOCUSS are presented. The results demonstrate that Shrinking LORETA-FOCUSS is able to reconstruct a three-dimensional source distribution with smaller localization and energy errors compared to the other methods.     

Performance of recursive suppression algorithm in nonstationaryenvironments

Adaptive superresolution algorithms possess the inherent ability to adapt to nonstationary environments. The recursive suppression algorithm is shown to provide much better resolution than the MUSIC algorithm when the average signal-to-noise ratios at array outputs are low and there are power variations or there is relative motion between the array and closely spaced signal sources. An implementation of the recursive suppression algorithm using digital signal processing is presented     

Source localization using recursively applied and projected (RAP)MUSIC

A new method for source localization is described that is based on a modification of the well-known MUSIC algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace. Errors in the estimate of the signal subspace can make localization of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection to find the next source is then performed in this reduced subspace. Special assumptions about the array manifold structure, such as Vandermonde or shift invariance, are not required. Using the metric of principal angles, we describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation with two highly correlated sources, we demonstrate the improved Monte Carlo error performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods: S and IES-MUSIC. We then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography (MEG) source localization simulation     

On the Use of a Calibration Emitter for Source Localization in the Presence of Sensor Position Uncertainty

Sensor position uncertainty is known to degrade significantly the source localization accuracy. This paper investigates the use of a single calibration emitter, whose position is known to the sensor array, to reduce the loss in localization accuracy due to sensor position errors that are random. Using a Gaussian noise model, we first derive the CramÉr–Rao lower bound (CRLB) for a time difference of arrival (TDOA)-based source location estimate with the use of a calibration source. The differential calibration technique that is commonly used in Global Positioning System through the use of a calibration source to mitigate the inaccuracy in satellite ephemeris data is analyzed. The analysis indicates that differential calibration in most cases cannot reach the CRLB accuracy. The paper then proceeds to propose an algebraic closed-form solution for the source location estimate using both TDOA measurements from the unknown and the calibration source. The proposed algorithm is shown analytically, under high signal-to-noise ratio (SNR) and small sensor position noise, or under moderate level of SNR and sensor position noise together with distant unknown and calibration sources, to reach the CRLB accuracy. Simulations are used to corroborate and support the theoretical development.      

一种任意信号源盲分离的高效算法

提出了信号源盲分离的DBBSS算法.利用随机变量概率密度函数非参数估计的核函数法,对混合信号的概率密度函数及其导数进行估计,并由此估计信号的评价函数(score function).解决了现有信号源盲分离算法中,普遍存在的非线性函数只能凭经验选取,以及混合信号同时包含超高斯信号和亚高斯信号时,算法失效的问题.该方法非常简单,可以直接应用于所有以非线性函数代替评价函数的信号源盲分离算法.仿真结果验证了算法的有效性.     

Efficient localization of synchronous EEG source activities using a modified RAP-MUSIC algorithm

Synchronization across different brain regions is suggested to be a possible mechanism for functional integration. Noninvasive analysis of the synchronization among cortical areas is possible if the electrical sources can be estimated by solving the electroencephalography inverse problem. Among various inverse algorithms, spatio-temporal dipole fitting methods such as RAP-MUSIC and R-MUSIC have demonstrated superior ability in the localization of a restricted number of independent sources, and also have the ability to reliably reproduce temporal waveforms. However, these algorithms experience difficulty in reconstructing multiple correlated sources. Accurate reconstruction of correlated brain activities is critical in synchronization analysis. In this study, we modified the well-known inverse algorithm RAP-MUSIC to a multistage process which analyzes the correlation of candidate sources and searches for independent topographies (ITs) among precorrelated groups. Comparative studies were carried out on both simulated data and clinical seizure data. The results demonstrated superior performance with the modified algorithm compared to the original RAP-MUSIC in recovering synchronous sources and localizing the epileptiform activity. The modified RAP-MUSIC algorithm, thus, has potential in neurological applications involving significant synchronous brain activities.     

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.     

Three-Dimension Localization of Wideband Sources Using Sensor Network

Usually source localization using sensor networks requires many sensors to localize a few number of sources, and it is still very troublesome to deal with coherent sources. When the three-dimensional (3-D) space are considered, the localization will become more difficult. A new approach is proposed to localize 3-D wideband coherent sources based on distributed sensor network, which consists of two nodes and each node contains only two sensors. Direction-of-arrival (DOA) estimation is performed at each node by employing a new noise subspace proposed. Combining the pattern matching idea and the prior geometrical information of sources, a cost function is constructed to estimate the rough positions. A rotational projection algorithm is proposed to estimate the heights of sources and correct the rough positions, and consequently the localization of 3-D sources could be achieved. Numerical examples are provided to demonstrate the effectiveness of this approach.