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     

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.     

Direction of arrival estimation of sources with intersecting signature in time–frequency domain using a combination of IF estimation and MUSIC algorithm

Time–frequency (TF) approaches are frequently employed for source localization at low signal to noise ratio. However, TF approaches fail to achieve the desired performance for sparsely sampled signals or signals corrupted by heavy noise in an under-determined scenario when sources are not TF separable. In this study, we propose a new TF method for direction of arrival (DOA) estimation of sources with closely spaced and overlapping TF signature. The proposed method uses a combination of a high-resolution time–frequency distribution and instantaneous frequency estimation method for extraction of sources with intersecting and closely spaced time–frequency signatures. Once sources are extracted, their DOAs are estimated using a well known multiple signal classification (MUSIC) algorithm. Experimental results demonstrate that the proposed source localization method achieves better performance as compared to the conventional time–frequency MUSIC algorithm.

     

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.     

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.     

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.     

Paired MEG data set source localization using recursively applied and projected (RAP) MUSIC

An important class of experiments in functional brain mapping involves collecting pairs of data corresponding to separate "Task" and "Control" conditions. The data are then analyzed to determine what activity occurs during the Task experiment but not in the Control. Here we describe a new method for processing paired magnetoencephalographic (MEG) data sets using our recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm. In this method the signal subspace of the Task data is projected against the orthogonal complement of the Control data signal subspace to obtain a subspace which describes spatial activity unique to the Task. A RAP-MUSIC localization search is then performed on this projected data to localize the sources which are active in the Task but not in the Control data. In addition to dipolar sources, effective blocking of more complex sources, e.g., multiple synchronously activated dipoles or synchronously activated distributed source activity, is possible since these topographies are well-described by the Control data signal subspace. Unlike previously published methods, the proposed method is shown to be effective in situations where the time series associated with Control and Task activity possess significant cross correlation. The method also allows for straightforward determination of the estimated time series of the localized target sources. A multiepoch MEG simulation and a phantom experiment are presented to demonstrate the ability of this method to successfully identify sources and their time series in the Task data.     

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.     

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     

Time-frequency MEG-MUSIC algorithm

We propose a method that incorporates the time-frequency characteristics of neural sources into magnetoencephalographic (MEG) source estimation. The method is based on the multiple-signal-classification (MUSIC) algorithm and it calculates a time--frequency matrix in which diagonal and off-diagonal terms are the auto and crosstime--frequency distributions of multichannel MEG recordings, respectively. The method averages this time-frequency matrix over the time--frequency region of interest. The locations of neural sources are then estimated by checking the orthogonality between the noise subspace of this averaged matrix and the sensor lead field. Accordingly, the method allows us to estimate the locations of neural sources from each time--frequency component. A computer simulation was performed to test the validity of the proposed method, and the results demonstrate its effectiveness.     

Oblique Projections for Direction-of-Arrival Estimation With Prior Knowledge

Estimation of directions-of-arrival (DOA) is an important problem in various applications and a priori knowledge on the source location is sometimes available. To exploit this information, standard methods are based on the orthogonal projection of the steering manifold onto the noise subspace associated with the a priori known DOA. In this paper, we derive and analyze the Cramer-Rao bound associated with this model and in particular we point out the limitations of this approach when the known and unknown DOA are closely spaced and the associated sources are uncorrelated (block-diagonal source covariance). To fill this need, we propose to integrate a priori known locations of several sources into the MUSIC algorithm based on oblique projection of the steering manifold. Finally, we show that the proposed approach is able to almost completely cancel the influence of the known DOA on the unknown ones for block-diagonal source covariance and for sufficient signal-to-noise ratio (SNR).     

Bayesian estimates of error bounds for EEG source imaging

Given a set of electrical potential measurements at the surface of the head, localizing the sources of the electrical activity is an inherently ill-posed problem. Bayesian methods can be used to specify prior information to constrain the possible source solutions. We show that Bayesian analysis can also provide a means for characterizing system noise levels, estimating the "error bars" surrounding source localization results, and estimating the information about brain processes conveyed by dense sensor array electroencephalographic (EEG) recordings. This method is, in principal, applicable to any linear model of EEG or magnetoencephalographic (MEG) processes. A series of simulations demonstrated the internal consistency of our method, the robustness to noise levels, and the limitations of accurate source localization with large numbers of sources.     

Near-field multiple source localization by passive sensor array

The localization of multiple near-field sources in a spatially white Gaussian noise environment is studied. A modified two-dimensional (2-D) version of the multiple signal classification (MUSIC) algorithm is used to localize the signal sources; range and bearing. A global-optimum maximum likelihood searching approach to localize these sources is discussed. It is shown that in the single source situation, the covariances of both the 2-D MUSIC estimator and the maximum likelihood estimator (MLE) approach the Cramer-Rao lower bound as the number of snapshots increases to infinity. In the multiple source situation, it is observed that for a high signal-to-noise ratio (SNR) and a large number of snapshots, the root mean square errors (RMSEs) of both localization techniques are relatively small. However, for low SNR and/or small number of snapshots, the performance of the MLE is much superior that of the modified 2-D MUSIC     

Statistical Performance of MUSIC-Like Algorithms in Resolving Noncircular Sources

This paper addresses the resolution of the conventional and noncircular MUSIC algorithms for arbitrary circular and noncircular second-order distributions of two uncorrelated closely spaced transmitters observed by an arbitrary array. An explicit closed-form expression of the mean null spectrum of the conventional and noncircular MUSIC algorithms is derived using an analysis based on perturbations of the noise projector instead of those of the eigenvectors. Based on these results, theoretical and approximate interpretable closed-form expressions of the threshold array signal-to-noise ratios (ASNR) at which these two algorithms are able to resolve two closely spaced transmitters along the Cox and the Sharman and Durrani criteria are given. It is proved that the threshold ASNRs given by the conventional MUSIC algorithm do not depend on the distribution of the sources including their noncircularity, in contrast to the noncircular MUSIC algorithm for which they are very sensitive to the noncircularity phase separation of the sources. This threshold ASNR given by the noncircular MUSIC algorithm is proven to be comfortably lower than that given by the conventional MUSIC algorithm except for weak phase separations of the sources for which the resolving powers of these two algorithms are very close. Finally, these results are analyzed through several illustrations and Monte Carlo simulations.      

Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction

This paper presents a new algorithm called Standardized Shrinking LORETA-FOCUSS (SSLOFO) for solving the electroencephalogram (EEG) inverse problem. Multiple techniques are combined in a single procedure to robustly reconstruct the underlying source distribution with high spatial resolution. This algorithm uses a recursive process which takes the smooth estimate of sLORETA as initialization and then employs the re-weighted minimum norm introduced by FOCUSS. An important technique called standardization is involved in the recursive process to enhance the localization ability. The algorithm is further improved by automatically adjusting the source space according to the estimate of the previous step, and by the inclusion of temporal information. Simulation studies are carried out on both spherical and realistic head models. The algorithm achieves very good localization ability on noise-free data. It is capable of recovering complex source configurations with arbitrary shapes and can produce high quality images of extended source distributions. We also characterized the performance with noisy data in a realistic head model. An important feature of this algorithm is that the temporal waveforms are clearly reconstructed, even for closely spaced sources. This provides a convenient way to estimate neural dynamics directly from the cortical sources.     

Parametric localization of distributed sources

Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method     

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.     

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.     

Near Field Source Separation Improvement Through Unconditional Maximum Likelihood Estimator

In this work, we are focused in the improvement of the near field source separation through the approach of the Unconditional Maximum Likelihood (UML) estimator. Four aspects are considered: separation sources, SNR variation, snapshots and multiple sources, in order to evaluate their influence in the capacity separation for the case of closely spaced sources. In this way, we can establish the minimum conditions for the sources separation. In addition, we investigated the effects of snapshots and the increasing number of sources in their spatial position estimation. Using Monte Carlo simulation, we obtained the Root Mean Square (RMS) error of the source’s direction of arrival. For evaluation purposes we include also MUSIC simulations. Our results show that the UML estimator improves source’s separation performance under low SNR and snapshot values as well as increasing number of sources.     

Novel high-resolution DOA estimation using subspace projection method

The performance of multiple signal classification(MUSIC) algorithm with regard to solving closely spaced direction of arrivals(DOAs) depends strongly upon the signal-to-noise ratio(SNR) and snapshots.In order to solve this problem,a method by reconstructing the spatial spectrum function with both noise subspace and signal subspace is presented in this paper.The key idea is to apply the full information contained in covariance matrix and change the projection weights of steering vector on the noise and signal subspace by their revised eigenvalues,respectively.Comparing with the MUSIC algorithm,it does not increase any computational complexity either,and remarkably,it has the advantages of simultaneously reducing noise and keeping the high-resolution ability under low SNR and small sample sized scenarios.Simulation and experiment results are included to demonstrate the superior performance of the proposed algorithm.