Keep it simple: a case for using classical minimum norm estimation in the analysis of EEG and MEG data

The present study aims at finding the optimal inverse solution for the bioelectromagnetic inverse problem in the absence of reliable a priori information about the generating sources. Three approaches to tackle this problem are compared theoretically: the maximum-likelihood approach, the minimum norm approach, and the resolution optimization approach. It is shown that in all three of these frameworks, it is possible to make use of the same kind of a priori information if available, and the same solutions are obtained if the same a priori information is implemented. In particular, they all yield the minimum norm pseudoinverse (MNP) in the complete absence of such information. This indicates that the properties of the MNP, and in particular, its limitations like the inability to localize sources in depth, are not specific to this method but are fundamental limitations of the recording modalities. The minimum norm solution provides the amount of information that is actually present in the data themselves, and is therefore optimally suited to investigate the general resolution and accuracy limits of EEG and MEG measurement configurations. Furthermore, this strongly suggests that the classical minimum norm solution is a valuable method whenever no reliable a priori information about source generators is available, that is, when complex cognitive tasks are employed or when very noisy data (e.g., single-trial data) are analyzed. For that purpose, an efficient and practical implementation of this method will be suggested and illustrated with simulations using a realistic head geometry.     

Visualization of magnetoencephalographic data using minimum current estimates.

The locations of active brain areas can be estimated from the magnetic field the neural current sources produce. In this work we study a visualization method of magnetoencephalographic data that is based on minimum[symbol: see text] (1)-norm estimates. The method can represent several local or distributed sources and does not need explicit a priori information. We evaluated the performance of the method using simulation studies. In a situation resembling typical magnetoencephalographic measurement, the mean estimated source strength exceeded baseline level up to 2 cm from the simulated point-like source. The method can also visualize several sources, activated simultaneously or in a sequence, which we demonstrated by analyzing magnetic responses associated with sensory stimulation and a picture naming task.     

Vector-based spatial-temporal minimum L1-norm solution for MEG

Minimum L1-norm solutions have been used by many investigators to analyze MEG responses because they provide high spatial resolution images. However, conventional minimum L1-norm approaches suffer from instability in spatial construction, and poor smoothness of the reconstructed source time-courses. Activity commonly "jumps" from one grid point to (usually) the neighboring grid points. Equivalently, the time-course of one specific grid point can show substantial "spiky-looking" discontinuity. In the present study, we present a new vector-based spatial-temporal analysis using a L1-minimum-norm (VESTAL). This approach is based on a principle of MEG physics: the magnetic waveforms in sensor-space are linear functions of the source time-courses in the imaging-space. Our computer simulations showed that VESTAL provides good reconstruction of the source amplitude and orientation, with high stability and resolution in both the spatial and temporal domains. "Spiky-looking" discontinuity was not observed in the source time-courses. Importantly, the simulations also showed that VESTAL can resolve sources that are 100% correlated. We then examined the performance of VESTAL in the analysis of human median-nerve MEG responses. The results demonstrated that this method easily distinguishes sources very spatially close to each other, including individual primary somatosensory areas (BA 1, 2, 3b), primary motor area (BA 4), and other regions in the somatosensory system (e.g., BA 5, 7, SII, SMA, and temporal-parietal junction) with high temporal stability and resolution. VESTAL's potential for obtaining information on source extent was also examined.     

Statistical shape analysis using non-Euclidean metrics

The contribution of this paper is the adaptation of data driven methods for non-Euclidean metric decomposition of tangent space shape coordinates. The basic idea is to extend principal component analysis (PCA) to take into account the noise variance at different landmarks and at different shapes. We show examples where these non-Euclidean metric methods allow for easier interpretation by decomposition into meaningful modes of variation. The extensions to PCA are based on adaptation of maximum autocorrelation factors and the minimum noise fraction transform to shape decomposition. A common basis of the methods applied is the assessment of the annotation noise variance at individual landmarks. These assessments are based on local models or repeated annotations by independent operators. We show that the Molgedey-Schuster independent component analysis is equivalent to the maximum autocorrelation factors. Finally, the different subspace methods are compared using a probabilistic formulation based on their ability to represent the data.     

Spatiotemporal dynamics of neural language processing: an MEG study using minimum-norm current estimates

The inferior frontal and superior temporal areas in the left hemisphere are well-known to be crucial for language processing in most right-handed individuals. This has been established by classical neurological investigations and neuropsychological studies along with metabolic brain imaging have recently revealed converging evidence. Here, we use fast neurophysiological brain imaging, magnetoencephalography (MEG), and L1 Minimum-Norm Current Estimates to investigate the time course of cortical activation underlying the magnetic Mismatch Negativity elicited by a spoken word. Left superior-temporal areas became active 136 ms after the information in the acoustic input was sufficient for identifying the word, and activation of the left inferior-frontal cortex followed after an additional delay of 22 ms. By providing answers to the where- and when-questions of cortical activation, MEG recordings paired with current estimates of the underlying cortical sources may advance our understanding of the spatiotemporal dynamics of distributed neuronal networks involved in cognitive processing in the human brain.     

Geometrical interpretation of fMRI-guided MEG/EEG inverse estimates

Magneto- and electroencephalography (MEG/EEG) and functional magnetic resonance imaging (fMRI) provide complementary information about the functional organization of the human brain. An important advantage of MEG/EEG is the millisecond time resolution in detecting electrical activity in the cerebral cortex. The interpretation of MEG/EEG signals, however, is limited by the difficulty of determining the spatial distribution of the neural activity. Functional MRI can help in the MEG/EEG source analysis by suggesting likely locations of activity. We present a geometric interpretation of fMRI-guided inverse solutions in which the MEG/EEG source estimate minimizes a distance to a subspace defined by the fMRI data. In this subspace regularization (SSR) approach, the fMRI bias does not assume preferred amplitudes for MEG/EEG sources, only locations. Characteristic dependence of the source estimates on the regularization parameters is illustrated with simulations. When the fMRI locations match the true MEG/EEG source locations, they serve to bias the underdetermined MEG/EEG inverse solution toward the fMRI loci. Importantly, when the fMRI loci do not match the true MEG/EEG loci, the solution is insensitive to those fMRI loci.     

基于独立成分分析和最小模解的眼电伪迹去除

目的：在采集到的脑电信号中分离并去除眼电伪迹，为临床应用和认知研究提供真实的脑电数据。方法：应用一种基于独立成分分析和最小模解的处理算法来去除眼电伪迹的影响。首先利用最小模解求解头表电位的皮质等效源分布，然后对皮质等效源进行独立成分分解，最后将分解后去除眼电伪迹的等效源还原为头皮数据。结果：利用独立成分分析分解等效源中眼电成分时比在头皮上更加准确，得到了所有电极在没有眼电成分即600～1600ms时间段内处理前后的数据相关系数。结论：基于独立成分分析和最小模解的处理算法可以实现在保证脑电信号完绍的前提下完全的去除眼电伪迹，能够在临床和认知研究中应用。     

Comparison of different metrics for analysis and visualization in spectroscopic optical coherence tomography

Spectroscopic Optical Coherence Tomography (S-OCT) extracts depth resolved spectra that are inherently available from OCT signals. The back scattered spectra contain useful functional information regarding the sample, since the light is altered by wavelength dependent absorption and scattering caused by chromophores and structures of the sample. Two aspects dominate the performance of S-OCT: (1) the spectral analysis processing method used to obtain the spatially-resolved spectroscopic information and (2) the metrics used to visualize and interpret relevant sample features. In this work, we focus on the second aspect, where we will compare established and novel metrics for S-OCT. These concepts include the adaptation of methods known from multispectral imaging and modern signal processing approaches such as pattern recognition. To compare the performance of the metrics in a quantitative manner, we use phantoms with microsphere scatterers of different sizes that are below the system’s resolution and therefore cannot be differentiated using intensity based OCT images. We show that the analysis of the spectral features can clearly separate areas with different scattering properties in multi-layer phantoms. Finally, we demonstrate the performance of our approach for contrast enhancement in bovine articular cartilage.OCIS codes: (170.4500) Optical coherence tomography, (300.0300) Spectroscopy, (290.5850) Scattering, particles, (180.0180) Microscopy, (170.3880) Medical and biological imaging     

基于独立成分分析和最小模解的眼电伪迹去除

目的:在采集到的脑电信号中分离并去除眼电伪迹,为临床应用和认知研究提供真实的脑电数据。方法:应用一种基于独立成分分析和最小模解的处理算法来去除眼电伪迹的影响。首先利用最小模解求解头表电位的皮质等效源分布,然后对皮质等效源进行独立成分分解,最后将分解后去除眼电伪迹的等效源还原为头皮数据。结果:利用独立成分分析分解等效源中眼电成分时比在头皮上更加准确,得到了所有电极在没有眼电成分即600～1600ms时间段内处理前后的数据相关系数。结论:基于独立成分分析和最小模解的处理算法可以实现在保证脑电信号完整的前提下完全的去除眼电伪迹,能够在临床和认知研究中应用。     

Lexical influences on speech perception: a Granger causality analysis of MEG and EEG source estimates

Behavioral and functional imaging studies have demonstrated that lexical knowledge influences the categorization of perceptually ambiguous speech sounds. However, methodological and inferential constraints have so far been unable to resolve the question of whether this interaction takes the form of direct top-down influences on perceptual processing, or feedforward convergence during a decision process. We examined top-down lexical influences on the categorization of segments in a /s/-/integral/ continuum presented in different lexical contexts to produce a robust Ganong effect. Using integrated MEG/EEG and MRI data we found that, within a network identified by 40 Hz gamma phase locking, activation in the supramarginal gyrus associated with wordform representation influences phonetic processing in the posterior superior temporal gyrus during a period of time associated with lexical processing. This result provides direct evidence that lexical processes influence lower level phonetic perception, and demonstrates the potential value of combining Granger causality analyses and high spatiotemporal resolution multimodal imaging data to explore the functional architecture of cognition.     

Multistart algorithms for MEG empirical data analysis reliably characterize locations and time courses of multiple sources

We applied our newly developed Multistart algorithm (M. Huang et al., 1998, Electroencephalogr. Clin. Neurophysiol. 108, 32-44) to high signal-to-noise ratio (SNR) somatosensory responses and low SNR visual data to demonstrate the reliability of this analysis tool for determining source locations and time courses of empirical multisource neuromagnetic data. This algorithm performs a downhill simplex search hundreds to thousands of times with multiple, randomly selected initial starting parameters from within the head volume, in order to avoid problems of local minima. Two subjects participated in two studies: (1) somatosensory (left and right median nerves were stimulated using a square wave pulse of 0.2 ms duration) and (2) visual (small black and white bull's-eye patterns were presented to central and peripheral locations in four quadrants of the visual field). One subject participated in both of the studies mentioned above and in a third study (i.e., simultaneous somatosensory/visual stimulation). The best-fitting solutions were tightly clustered in high SNR somatosensory data and all dominant regions of activity could be identified in some instances by using a single model order (e.g., six dipoles) applied to a single interval of time (e.g., 15-250 ms) that captured the entire somatosensory response. In low SNR visual data, solutions were obtained from several different model orders and time intervals in order to capture the dominant activity across the entire visual response (e.g. , 60-300 ms). Our results demonstrate that Multistart MEG analysis procedures can localize multiple regions of activity and characterize their time courses in a reliable fashion. Sources for visual data were determined by comparing results across several different models, each of which was based on hundreds to thousands of different fits to the data.     

Time-frequency discriminant analysis of MEG signals

This paper introduces a novel statistical method that can identify relevant time-frequency features in brain signals to distinguish between groups. The feature of interest is the spectrum which characterizes the distribution of a given signal's variance (or power) across frequency oscillations. Brain signals are generally nonstationary in that the distribution of the signals' power across frequency changes over time. The classical Fourier analysis is not formally suitable for time series signals with time-varying spectra. This paper utilizes the SLEX (Smooth Localized Complex EXponentials) basis function to capture the transient features of brain signals. The SLEX basis consists of a set of localized orthogonal Fourier-like waveforms with a built-in mechanism for representing localized spectral features. The best basis is first chosen that maximizes group dissimilarity in the time-varying spectra. However, not all spectral features extracted from the best basis may be useful for discrimination and classification purpose. A thresholding scheme is further developed to remove irrelevant features from the best basis to improve accuracy for classification. In simulations the proposed SLEX-thresholding discriminant method was able to consistently identify the most discriminant time-frequency features and was able to correctly classify signals at a high rate. The method was then applied to magnetoencephalographic data from a standard paired-click paradigm. Discrimination between individuals with schizophrenia and a healthy comparison group confirmed the utility of the method.     

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

This paper discusses the location bias and the spatial resolution in the reconstruction of a single dipole source by various spatial filtering techniques used for neuromagnetic imaging. We first analyze the location bias for several representative adaptive and non-adaptive spatial filters using their resolution kernels. This analysis theoretically validates previously reported empirical findings that standardized low-resolution electromagnetic tomography (sLORETA) has no location bias. We also find that the minimum-variance spatial filter does exhibit bias in the reconstructed location of a single source, but that this bias is eliminated by using the normalized lead field. We then focus on the comparison of sLORETA and the lead-field normalized minimum-variance spatial filter, and analyze the effect of noise on source location bias. We find that the signal-to-noise ratio (SNR) in the measurements determines whether the sLORETA reconstruction has source location bias, while the lead-field normalized minimum-variance spatial filter has no location bias even in the presence of noise. Finally, we compare the spatial resolution for sLORETA and the minimum-variance filter, and show that the minimum-variance filter attains much higher resolution than sLORETA does. The results of these analyses are validated by numerical experiments as well as by reconstructions based on two sets of evoked magnetic responses.     

Spatiotemporal Bayesian inference dipole analysis for MEG neuroimaging data

Recently, we described a Bayesian inference approach to the MEG/EEG inverse problem that used numerical techniques to estimate the full posterior probability distributions of likely solutions upon which all inferences were based [Schmidt, D.M., George, J.S., Wood, C.C., 1999. Bayesian inference applied to the electromagnetic inverse problem. Human Brain Mapping 7, 195; Schmidt, D.M., George, J.S., Ranken, D.M., Wood, C.C., 2001. Spatial-temporal bayesian inference for MEG/EEG. In: Nenonen, J., Ilmoniemi, R. J., Katila, T. (Eds.), Biomag 2000: 12th International Conference on Biomagnetism. Espoo, Norway, p. 671]. Schmidt et al. (1999) focused on the analysis of data at a single point in time employing an extended region source model. They subsequently extended their work to a spatiotemporal Bayesian inference analysis of the full spatiotemporal MEG/EEG data set. Here, we formulate spatiotemporal Bayesian inference analysis using a multi-dipole model of neural activity. This approach is faster than the extended region model, does not require use of the subject's anatomical information, does not require prior determination of the number of dipoles, and yields quantitative probabilistic inferences. In addition, we have incorporated the ability to handle much more complex and realistic estimates of the background noise, which may be represented as a sum of Kronecker products of temporal and spatial noise covariance components. This reduces the effects of undermodeling noise. In order to reduce the rigidity of the multi-dipole formulation which commonly causes problems due to multiple local minima, we treat the given covariance of the background as uncertain and marginalize over it in the analysis. Markov Chain Monte Carlo (MCMC) was used to sample the many possible likely solutions. The spatiotemporal Bayesian dipole analysis is demonstrated using simulated and empirical whole-head MEG data.     

Independent component analysis of short-time Fourier transforms for spontaneous EEG/MEG analysis

Analysis of spontaneous EEG/MEG needs unsupervised learning methods. While independent component analysis (ICA) has been successfully applied on spontaneous fMRI, it seems to be too sensitive to technical artifacts in EEG/MEG. We propose to apply ICA on short-time Fourier transforms of EEG/MEG signals, in order to find more “interesting” sources than with time-domain ICA, and to more meaningfully sort the obtained components. The method is especially useful for finding sources of rhythmic activity. Furthermore, we propose to use a complex mixing matrix to model sources which are spatially extended and have different phases in different EEG/MEG channels. Simulations with artificial data and experiments on resting-state MEG demonstrate the utility of the method.     

A space-frequency analysis of MEG background processes

In MEG source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account. Since this covariance is in general too large to estimate based on the data and to invert efficiently, different parametrizations have been proposed in the literature. These models can be seen as special cases of the general decomposition of the covariance into a sum of Kronecker products of spatial matrices X(n) and temporal matrices T(n) (Van Loan, 2000). In this study we investigate the assumption of the matrices T(n) being Toeplitz. If so, the covariance matrix in the space-frequency domain will have an approximate block-diagonal structure, facilitating inversion, which is a prerequisite for source localization. In this study we address the question whether the Toeplitz approximation is valid for data sets obtained in visual evoked field, auditory evoked field, somatosensory evoked field experiments and data sets containing spontaneous activity. It turns out that on average 87% is in the block-diagonal of the sample covariance, which is close to the values obtained for real Toeplitz matrices T(n). This implies that the space-frequency domain is very interesting for source localization since the major part of the entire covariance can be incorporated in that domain straightforwardly. Finally, the two major processes in the background activity are characterized in terms of their spatial and frequency patterns, yielding a focal and a non-focal pattern in 8 of 10 data sets analyzed in this study. The focal pattern represents the alpha frequency at parieto-occipital areas, whereas the non-focal pattern is more widespread both in space and in frequency.     

ICA-based spatiotemporal approach for single-trial analysis of postmovement MEG beta synchronization

The extraction of event-related oscillatory neuromagnetic activities from single-trial measurement is challenging due to the non-phase-locked nature and variability from trial to trial. The present study presents a method based on independent component analysis (ICA) and the use of a template-based correlation approach to extract Rolandic beta rhythm from magnetoencephalographic (MEG) measurements of right finger lifting. A single trial recording was decomposed into a set of coupled temporal independent components and corresponding spatial maps using ICA and the reactive beta frequency band for each trial identified using a two-spectrum comparison between the postmovement interval and a reference period. Task-related components survived dual criteria of high correlation with both the temporal and the spatial templates with an acceptance rate of about 80%. Phase and amplitude information for noise-free MEG beta activities were preserved not only for optimal calculation of beta rebound (event-related synchronization) but also for profound penetration into subtle dynamics across trials. Given the high signal-to-noise ratio (SNR) of this method, various methods of source estimation were used on reconstructed single-trial data and the source loci coherently anchored in the vicinity of the primary motor area. This method promises the possibility of a window into the intricate brain dynamics of motor control mechanisms and the cortical pathophysiology of movement disorder on a trial-by-trial basis.     

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

Beamformers are a commonly used method for doing source localization from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beamformer output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.     

Rationale for using multiple regression analysis with complex interferences.

Non-specificities and interferences may become complex when they involve the analyte as well as other interfering substances. These non-specificities and interferences are known as analyte-dependent and multi-interferent interferences. Multiple regression analysis has proven valuable in analysing this type of interference, but the theoretical foundation for using multiple regression analysis to study the basic mechanisms of interference has not been explicitly demonstrated. Graph theory can depict and model the basic mechanisms of interferences and the possible interactions. The relationship between the analyte, the interferents, and the response of the instrument to these entities can be approximated by a polymial of order three, which includes partial derivatives and cross-terms. The partial derivatives relate to the different interactions found with the graph theory model. Further, the partial derivatives can be associated with the coefficients in the multiple regression analysis when the respective values of the three variables (analyte, interferent one, and interferent two) are multiplied by one another. One can decide to retain or discard the coefficient of a variable, based on the statistical significance of the coefficient. The respective interactions in the graphic model can then be assembled and the framework of the interference mechanism established.