Spatio-temporal EEG source localization using simulated annealing

The estimation of multiple dipole parameters in spatio-temporal source modeling (STSM) of electroencephalographic (EEG) data is a difficult nonlinear optimization problem due to multiple local minima in the cost function. A straightforward iterative optimization approach to such a problem is very susceptible to being trapped in a local minimum, thereby resulting in incorrect estimates of the dipole parameters. Here, the authors present and evaluate a more robust optimization approach based on the simulated annealing algorithm. The complexity of this approach for the STSM problem was reduced by separating the dipole parameters into linear (moment) and nonlinear (location) components. The effectiveness of the proposed method and its superiority over the traditional nonlinear simplex technique in escaping local minima were tested and demonstrated through computer simulations. The annealing algorithm and its implementation for multidipole estimation are also discussed. The authors found the simulated annealing approach to be 7-31% more effective than the simplex method at converging to the true global minimum for a number of different kinds of three-dipole problems simulated in this work. In addition, the computational cost of the proposed approach was only marginally higher than its simplex counterpart. The annealing method also yielded similar solutions irrespective of the initial guesses used. The proposed simulated annealing method is an attractive alternative to the simplex method that is currently more common in dipole estimation applications     

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.     

MEG and EEG source localization in beamspace

Beamspace methods are applied to EEG/MEG source localization problems in this paper. Beamspace processing involves passing the data through a linear transformation that reduces the data dimension prior to applying a desired statistical signal processing algorithm. This process generally reduces the data requirements of the subsequent algorithm. We present one approach for designing beamspace transformations that are optimized to preserve source activity located within a given region of interest and show that substantial reductions in dimension are obtained with negligible signal loss. Beamspace versions of maximum likelihood dipole fitting, MUSIC, and minimum variance beamforming source localization algorithms are presented. The performance improvement offered by the beamspace approach with limited data is demonstrated by bootstrapping somatosensory data to evaluate the variability of the source location estimates obtained with each algorithm. The quantitative benefits of beamspace processing depend on the algorithm, signal to noise ratio, and amount of data. Dramatic performance improvements are obtained in scenarios with low signal to noise ratio and a small number of independent data samples.     

Statistical maps for EEG dipolar source localization

We present a method that estimates three-dimensional statistical maps for electroencephalogram (EEG) source localization. The maps assess the likelihood that a point in the brain contains a dipolar source, under the hypothesis of one, two or three activated sources. This is achieved by examining all combinations of one to three dipoles on a coarse grid and attributing to each combination a score based on an F statistic. The probability density function of the statistic under the null hypothesis is estimated nonparametrically, using bootstrap resampling. A theoretical F distribution is then fitted to the empirical distribution in order to allow correction for multiple comparisons. The maps allow for the systematic exploration of the solution space for dipolar sources. They permit to test whether the data support a given solution. They do not rely on the assumption of uncorrelated source time courses. They can be compared to other statistical parametric maps such as those used in functional magnetic resonance imaging (fMRI). Results are presented for both simulated and real data. The maps were compared with LORETA and MUSIC results. For the real data consisting of an average of epileptic spikes, we observed good agreement between the EEG statistical maps, intracranial EEG recordings, and fMRI activations.     

Distributed source localization using ESPRIT algorithm

A new algorithm based on ESPRIT is proposed for the estimation of the central angle and angular extension of distributed sources. The central angles are estimated using TLS-ESPRIT for both incoherently distributed (ID) and coherently distributed (CD) sources. For CD sources, the extension width is estimated by constructing a one-dimensional (1-D) distributed source parameter estimator (DSPE) spectrum for each source. For ID sources, the extension widths are estimated using the central moments of the distribution. The algorithm can be used for sources with different angular distributions     

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     

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.     

EEG localization accuracy improvements using realistically shapedhead models

A model of the head must be used in making estimates of the locations of electrical sources in the brain using electroencephalograms (EEGs) measured on the scalp. In part, the accuracy of these estimates is dependent on how accurately the model represents the actual head. In most work performed to date, spherical models of the head have been used. This paper presents results in which the estimates of source location are made in realistically shaped head models. Techniques for accurately and conveniently developing realistically shaped head models from CTs, MRIs, X-rays, and/or physical measurements are also presented. Realistically shaped head models are developed for three subjects with electrical sources implanted at known locations in the brain. Localization accuracy is found to be significantly better in the realistically shaped bead models than in spherical models if EEGs with good signal-to-noise ratio are used     

Efficient wideband source localization using beamforming invariancetechnique

A novel scheme for wideband direction-of-arrival (DOA) estimation is proposed. The technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices. The beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency, regardless of the actual spatial distribution of the sources. The focused data correlation matrix can thus be obtained without any preliminary DOA estimation or iteration. A simplified version of the beamspace Root-MUSIC algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear, equally spaced array. Numerical simulations are conducted to demonstrate the efficacy of the new scheme     

An efficient algorithm for computing multishell spherical volumeconductor models in EEG dipole source localization

Computationally localizing electrical current sources of the electroencephalographic signal requires a volume conductor model which relates theoretical scalp potentials to the dipolar source located within the modeled brain. The commonly used multishell spherical model provides this source-potential relationship using a sum of infinite series whose computation is difficult. This paper provides a closed-form approximation to this sum based on an optimal fitting to the weights of the Legendre polynomials. The second-order (third-order) approximation algorithm, implemented by a provided C-routine, requires only 100 (140) floating point operations to compute a single scalp potential in response to an arbitrary current dipole located within a four-shell spherical volume conductor model. This cost of computation represents only 6.3% (8.9%) of that required by the direct method. The relative mean square error, measured by using 20,000 random dipoles distributed within the modeled brain, is only 0.29% (0.066%)     

Wideband source localization using a distributed acoustic vector-sensor array

We derive fast wideband algorithms, based on measurements of the acoustic intensity, for determining the bearings of a target using an acoustic vector sensor (AVS) situated in free space or on a reflecting boundary. We also obtain a lower bound on the mean-square angular error (MSAE) of such estimates. We then develop general closed-form weighted least-squares (WLS) and reweighted least-squares algorithms that compute the three-dimensional (3-D) location of a target whose bearing to a number of dispersed locations has been measured. We devise a scheme for adaptively choosing the weights for the WLS routine when measures of accuracy for the bearing estimates, such as the lower bound on the MSAE, are available. In addition, a measure of the potential estimation accuracy of a distributed system is developed based on a two-stage application of the Cramer-Rao bound. These 3-D results are quite independent of how bearing estimates are obtained. Naturally, the two parts of the paper are tied together by examining how well distributed arrays of AVSs located on the ground, seabed, and in free space can determine the 3-D position of a target The results are relevant to the localization of underwater and airborne sources using freely drifting, moored, or ground sensors. Numerical simulations illustrate the effectiveness of our estimators and the new potential performance measure.     

Wideband source localization using sparse learning via iterative minimization

In this paper, two extensions of the Sparse Learning via Iterative Minimization (SLIM) algorithm are presented for wideband source localization using a sensor array. The proposed methods exploit the joint sparse structure across all frequency bins, and estimate the spatial pseudo-spectra at various frequency bins jointly and iteratively. Via several numerical examples, we show that the proposed methods can provide high-resolution angle estimates and excellent source localization performance, and are able to resolve the left–right ambiguity problem, when used together with the vector sensor array technology.     

Multiplexing of optical fiber sensors using a frequency-modulated source and gated output

A novel method is proposed and demonstrated for multiplexing fiber-optic interferometric sensors using the FMCW technique. The method uses a gas laser whose optical frequency is modulated sinusoidally by an external modulator. The use of gating and appropriate signal processing can achieve low crosstalk between sensors. Experiments on two and three sensor systems are reported. The minimum detectable signal measured is 1 mrad/sqrt{Hz}and the crosstalk factor achieved is -35 dB. The major causes of crosstalk are also analyzed.     

一种用于分布式阵列的球谐波域声源定位方法

本文提出一种适用于任意阵型和阵元指向性的球谐波域声源定位方法,能够在较宽的频域范围内,尤其是低频,提供较高的空间分辨率。水下噪声源的高分辨识别具有重大意义。传统阵列信号处理方法对低频噪声源的精确定位要求阵列具有较大孔径和较多的阵元数,导致系统过于庞大且成本较高。我们基于声场的球谐波表达和变换,采用分布在一定空间区域内的多个阵列估计该区域的球谐波系数矢量,对系数矢量进行信号处理实现声源定位。理论证明了该方法具有理想的空间选择特性。在一种特定的阵元分布下,仿真研究了该算法的方位谱估计性能以及阵元不一致性和位置误差对声源定位性能的影响。仿真结果显示,该算法在低频具有较高的空间分辨率且误差对算法定位性能的影响有限。      

一种多脉冲联合处理的塔康辐射源定位方法

根据塔康（TACAN）脉冲序列的连续性,提出了一种基于多脉冲联合测向定位的新方法。该方法仅需两个相距较远的天线阵元,先利用塔康脉冲的特征,建立单个脉冲和多个脉冲间对应的侦测平台、目标飞机以及塔康信标台三者位置关系方程,得到目标方位初始解;利用该初始解,对两阵元干涉仪测向解模糊,得到方位角的高精度解,再代入时差-方位双曲线方程得到目标位置的高精度解。该方法相比传统方法有更高的测向定位精度和更简化的天线布局,有利于工程应用推广。     

Statistical performance analysis of signal variance-based dipole models for MEG/EEG source localization and detection

A set of dipole fitting algorithms that incorporate different assumptions about the variability of the signal component into their mathematical models is presented and analyzed. Dipole fitting is performed by minimizing the squared error between the selected data model and available data. Dipole models based on moments that have 1) constant amplitude and orientation, 2) variable amplitude and fixed known orientation, 3) variable amplitude and fixed unknown orientation, and 4) variable amplitude and variable orientation are considered. The presence of a dipolar source is determined by comparing the fractional energy explained by the dipole model to a threshold. Source localization is accomplished by searching to find the location that explains the largest fractional signal energy using a dipole model. Expressions for the probability of a false positive decision and probability of correct detection are derived and used to evaluate the effect of variability in the dipole on performance and to address the effects of model mismatch and location errors. Simulated and measured data experiments are presented to illustrate the performance of both detection and localization methods. The results indicate that models which account for variance outperform the constant orientation and magnitude model even when the number of observations is relatively small and the signal of interest contains a very modest variance component.     

High-resolution CCD image sensors with reduced smear

Two types of interline transfer CCD image sensors with reduced smear signal were developed, one for a 525-line TV system (EIA) and one for a 625-line system (CCIR). An MOS diode is employed as a sensing element to realize negligibly small lag compared with that of a junction diode. The EIA and CCIR version have effective number of pixels of 510 × 492 and 500 × 582, respectively. Smear is reduced down to -92 dB by fabricating the vertical shift register on the p-well. In spite of the shrunken element area, the blue sensitivity similar to that for a conventional 384 × 491 CCD imager [1] is obtained by optimization of the film thickness on the diode. Resolution as high as 330 TV lines in color is also attained.     

多校准站TDOA/FDOA无源定位方法

针对运动目标到达时差（Time Difference-of-Arrival,TDOA）/到达频差（Frequency Difference-of-Arrival,FDOA）定位中的接收站定位误差问题,提出了基于多校准站的TDOA/FDOA定位方法,有效降低接收站定位误差的影响,并推导了该方法的克拉美罗下限（Cramér-Rao Lower Bound,CRLB）。理论分析表明,采用多校准站法能有效降低CRLB,提高目标定位精度。同时,当校准站自身定位存在误差时,也将影响对接收站的校准和目标的定位精度。通过仿真实验定量分析了采用多校准站法对定位精度的改善程度。     

Concurrent speakers localization using blind source separation and microphone array geometry

Multidimensional Systems and Signal Processing - Speaker localization has been an active topic of research due to its wide range of applications in multimedia and communication technologies. While...     

MEG source localization using an MLP with a distributed output representation

We present a system that takes realistic magnetoencephalographic (MEG) signals and localizes a single dipole to reasonable accuracy in real time. At its heart is a multilayer perceptron (MLP) which takes the sensor measurements as inputs, uses one hidden layer, and generates as outputs the amplitudes of receptive fields holding a distributed representation of the dipole location. We trained this Soft-MLP on dipolar sources with real brain noise and converted the network's output into an explicit Cartesian coordinate representation of the dipole location using two different decoding strategies. The proposed Soft-MLPs are much more accurate than previous networks which output source locations in Cartesian coordinates. Hybrid Soft-MLP-start-LM systems, in which the Soft-MLP output initializes Levenberg-Marquardt, retained their accuracy of 0.28 cm with a decrease in computation time from 36 ms to 30 ms. We apply the Soft-MLP localizer to real MEG data separated by a blind source separation algorithm, and compare the Soft-MLP dipole locations to those of a conventional system.