A signal subspace approach for modeling the hemodynamic response function in fMRI

Many fMRI analysis methods use a model for the hemodynamic response function (HRF). Common models of the HRF, such as the Gaussian or Gamma functions, have parameters that are usually selected a priori by the data analyst. A new method is presented that characterizes the HRF over a wide range of parameters via three basis signals derived using principal component analysis (PCA). Covering the HRF variability, these three basis signals together with the stimulation pattern define signal subspaces which are applicable to both linear and nonlinear modeling and identification of the HRF and for various activation detection strategies. Analysis of simulated fMRI data using the proposed signal subspace showed increased detection sensitivity compared to the case of using a previously proposed trigonometric subspace. The methodology was also applied to activation detection in both event-related and block design experimental fMRI data using both linear and nonlinear modeling of the HRF. The activated regions were consistent with previous studies, indicating the ability of the proposed approach in detecting brain activation without a priori assumptions about the shape parameters of the HRF. The utility of the proposed basis functions in identifying the HRF is demonstrated by estimating the HRF in different activated regions.     

Statistical methods for detecting activated regions in functional MRI of the brain

Two statistical tests for detecting activated pixels in functional MRI (fMRI) data are presented. The first test (t-test) is the optimal solution to the problem of detecting a known activation signal in Gaussian white noise. The results of this test are shown to be equivalent to the cross-correlation method that is widely used for activation detection in fMRI. The second test (F test) is the optimal solution when the measured data are modeled to consist of an unknown activation signal that lies in a known lower dimensional subspace of the measurement space with added Gaussian white noise. A model for the signal subspace based on a truncated trigonometric Fourier series is proposed for periodic activation–baseline imaging paradigms. The advantage of the second method is that it does not assume any information about the shape or delay of the activation signal, except that it is periodic with the same period as the activation–baseline pattern. The two models are applied to experimental echo-planar fMRI data sets and the results are compared.     

Cross-correlation dynamics in financial time series

The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined.A basic one-factor model is then proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a ‘market plus sectors’ model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data. By partitioning the eigenvalue time series, we then show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. The study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies.     

A novel local PCA-based method for detecting activation signals in fMRI.

A novel local principal component analysis (LPCA) technique is presented for activation signal detection in functional magnetic resonance imaging (fMRI) without explicit knowledge about the shape of the model activation signal. Unlike the traditional PCA methods, our LPCA algorithm is based on a measure of separation between two clusters formed by the signal segments in active periods and inactive periods, which is computed in an eigen-subspace. In addition, we only applied PCA to the temporal sequence of each individual voxel instead of applying PCA to the fMRI data set. In our algorithm, we first applied a linear regression procedure to alleviate the baseline drift artifact. Then, the baseline-corrected temporal signals were partitioned into active and inactive segments according to the paradigm used for the fMRI data acquisition. Principal components were computed from all these segments for each voxel by PCA. By projecting the segments of each voxel onto a linear subspace formed by the corresponding most dominant principal components, two separate clusters were formed from active and inactive segments. An activation measure was defined based on the degree of separation between these two clusters in the projection space. We show experimental results on the activation signal detection from various sets of fMRI data with different types of stimulation by using the proposed LPCA algorithm and the standard t-test method for comparison. Our experiments indicate that the LPCA algorithm in general provides substantial signal-to-noise ratio improvement over the t-test method.     

Principal component analysis of the dynamic response measured by fMRI: a generalized linear systems framework.

Principal component analysis (PCA) is one of several structure-seeking multivariate statistical techniques, exploratory as well as inferential, that have been proposed recently for the characterization and detection of activation in both PET and fMRI time series data. In particular, PCA is data driven and does not assume that the neural or hemodynamic response reaches some steady state, nor does it involve correlation with any pre-defined or exogenous experimental design template. In this paper, we present a generalized linear systems framework for PCA based on the singular value decomposition (SVD) model for representation of spatio-temporal fMRI data sets. Statistical inference procedures for PCA, including point and interval estimation will be introduced without the constraint of explicit hypotheses about specific task-dependent effects. The principal eigenvectors capture both the spatial and temporal aspects of fMRI data in a progressive fashion; they are inherently matched to unique and uncorrelated features and are ranked in order of the amount of variance explained. PCA also acts as a variation reduction technique, relegating most of the random noise to the trailing components while collecting systematic structure into the leading ones. Features summarizing variability may not directly be those that are the most useful. Further analysis is facilitated through linear subspace methods involving PC rotation and strategies of projection pursuit utilizing a reduced, lower-dimensional natural basis representation that retains most of the information. These properties will be illustrated in the setting of dynamic time-series response data from fMRI experiments involving pharmacological stimulation of the dopaminergic nigro-striatal system in primates.     

Estimation of the number of endmembers in hyperspectral data using a weight-sequence geometry method

The terrestrial reflection or emission spectrum obtained by the remote sensor is recorded in units of pixels. In most cases, a pixel usually contains many types of terrains. This pixel is a mixed pixel, and each of the terrains in the mixed pixels is called “endmember”. Estimating the number of endmembers is a significant step in many hyperspectral data mining techniques, such as target classification and endmember extraction. The paper proposes a separative detection method by the use of a weight-sequence geometry to estimate the number of endmembers. This method projects the spectral matrix into the orthogonal subspace by eigenvalue decomposition at first. Then, on the basis of the normalized eigenvalue sequence, the separative detection method innovatively uses a geometric criterion to find the separation point between the main factors and minor factors. Finally, the number of endmembers is determined by the sequence of the “separation point”. Validation through a series of simulated and real hyperspectral data, it indicates that the proposed method can accurately and rapidly detect the number of endmembers in the hyperspectral data without any prior information. In addition, the new method is also applicable to the ultra-high resolution remote spectral data in the future.     

Comparing the structure of an emerging market with a mature one under global perturbation

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.     

Evaluation and optimization of fMRI single-subject processing pipelines with NPAIRS and second-level CVA

In functional magnetic resonance imaging (fMRI) analysis, although the univariate general linear model (GLM) is currently the dominant approach to brain activation detection, there is growing interest in multivariate approaches such as principal component analysis, canonical variate analysis (CVA), independent component analysis and cluster analysis, which have the potential to reveal neural networks and functional connectivity in the brain. To understand the effect of processing options on performance of multivariate model-based fMRI processing pipelines with real fMRI data, we investigated the impact of commonly used fMRI preprocessing steps and optimized the associated multivariate CVA-based, single-subject processing pipelines with the NPAIRS (nonparametric prediction, activation, influence and reproducibility resampling) performance metrics [prediction accuracy and statistical parametric image (SPI) reproducibility] on the Fiswidgets platform. We also compared the single-subject SPIs of univariate GLM with multivariate CVA-based processing pipelines from SPM, FSL.FEAT, NPAIRS.GLM and NPAIRS.CVA software packages (or modules) using a novel second-level CVA. We found that for the block-design data, (a) slice timing correction and global intensity normalization have little consistent impact on the fMRI processing pipeline, but spatial smoothing, temporal detrending or high-pass filtering, and motion correction significantly improved pipeline performance across all subjects; (b) the combined optimization of spatial smoothing, temporal detrending and CVA model parameters on average improved between-subject reproducibility; and (c) the most important pipeline choices include univariate or multivariate statistical models and spatial smoothing. This study suggests that considering options other than simply using GLM with a fixed spatial filter may be of critical importance in determining activation patterns in BOLD fMRI studies.     

Comprehensive mathematical simulation of functional magnetic resonance imaging time series including motion-related image distortion and spin saturation effect

There has been vast interest in determining the feasibility of functional magnetic resonance imaging (fMRI) as an accurate method of imaging brain function for patient evaluations. The assessment of fMRI as an accurate tool for activation localization largely depends on the software used to process the time series data. The performance evaluation of different analysis tools is not reliable unless truths in motion and activation are known. Lack of valid truths has been the limiting factor for comparisons of different algorithms. Until now, currently available phantom data do not include comprehensive accounts of head motion. While most fMRI studies assume no interslice motion during the time series acquisition in fMRI data acquired using a multislice and single-shot echo-planar imaging sequence, each slice is subject to a different set of motion parameters. In this study, in addition to known three-dimensional motion parameters applied to each slice, included in the time series computation are geometric distortion from field inhomogeneity and spin saturation effect as a result of out-of-plane head motion. We investigated the effect of these head motion-related artifacts and present a validation of the mapping slice-to-volume (MSV) algorithm for motion correction and activation detection against the known truths. MSV was evaluated, and showed better performance in comparison with other widely used fMRI data processing software, which corrects for head motion with a volume-to-volume realignment method. Furthermore, improvement in signal detection was observed with the implementation of the geometric distortion correction and spin saturation effect compensation features in MSV.     

Dissecting cognitive stages with time-resolved fMRI data: a comparison of fuzzy clustering and independent component analysis

In combination with cognitive tasks entailing sequences of sensory and cognitive processes, event-related acquisition schemes allow using functional MRI to examine not only the topography but also the temporal sequence of cortical activation across brain regions (time-resolved fMRI). In this study, we compared two data-driven methods--fuzzy clustering method (FCM) and independent component analysis (ICA)--in the context of time-resolved fMRI data collected during the performance of a newly devised visual imagery task. We analyzed a multisubject fMRI data set using both methods and compared their results in terms of within- and between-subject consistency and spatial and temporal correspondence of obtained maps and time courses. Both FCM and spatial ICA allowed discriminating the contribution of distinct networks of brain regions to the main cognitive stages of the task (auditory perception, mental imagery and behavioural response), with good agreement across methods. Whereas ICA worked optimally on the original time series, averaging with respect to the task onset (and thus introducing some a priori information on the stimulation protocol) was found to be indispensable in the case of FCM. On averaged time series, FCM led to a richer decomposition of the spatio-temporal patterns of activation and allowed a finer separation of the neurocognitive processes subserving the mental imagery task. This study confirms the efficacy of the two examined methods in the data-driven estimation of hemodynamic responses in time-resolved fMRI studies and provides empirical guidelines to their use.     

基于随机矩阵理论的城市人群移动行为分析

移动通信应用为人类移动规律的研究提供了独特的数据来源. 本文通过城市手机用户的分布数据,研究城市移动人群的整体动力学行为. 借助随机矩阵理论的方法,通过比较移动人群数据与随机数据在互相关矩阵谱分布上的差异,发现移动人群数据互相关矩阵的相关系数均值、最大本征值及其对应的本征向量明显偏离于随机互相关矩阵的分布,指出这种差异体现了城市移动人群的整体行为特性,且这种差异在不同时间段也会有所不同. 研究结果体现出相关系数的均值和最大本征值的波动趋势,并指出本征向量成员权重的时空模式与城市移动人群整体行为特征的波动过 关键词： 随机矩阵理论 移动人群 宏观行为     

A method for comparing group fMRI data using independent component analysis: application to visual, motor and visuomotor tasks

Independent component analysis (ICA) is an approach for decomposing fMRI data into spatially independent maps and time courses. We have recently proposed a method for ICA of multisubject data; in the current paper, an extension is proposed for allowing ICA group comparisons. This method is applied to data from experiments designed to stimulate visual cortex, motor cortex or both visual and motor cortices. Several intergroup and intragroup metrics are proposed for assessing the utility of the components for comparisons of group ICA data. The proposed method may prove to be useful in answering questions requiring multigroup comparisons when a flexible modeling approach is desired.     

Iterative inverse beamforming algorithm and its application in multiple targets detection of passive sonar

With the increasing of detection ability of passive sonar,the weak signal detection problem in multiple interferences becomes more and more important.In the time/bearing record(TBR) display of sonar detection,when there exist traces of multiple interferences,the identification of weak signal is difficult or impossible.The adaptive noise cancellation technique provides the theoretical basis for suppressing strong interferences.But the solution for finding the steady-state optimum filter matrix is quite difficult due to the real time calculation of inverse matrix of input data correlation matrix.The iterative inverse beamforming(IBF) algorithm for solving the optimum filter vector,which is expressed by inverse matrix of the ocean environment data,is derived in this paper,by which,the optimum filter can be eventually expressed as a sum of series simple matrices of constructed from sensor data.Based on the algorithm proposed in this paper,some examples of at sea experiment are provided.The strong interferences are cancelled and the weak signal is emerged,even it didn't appear in the conventional beamforming(CBF) processing.     

无源声呐多目标检测中反波束成形递推算法及其应用

随着声呐检测能力的提高,多目标干扰下微弱信号的检测问题日益突出。当声呐方位历程显示上出现多个干扰轨迹时,弱目标的检测显得十分困难。自适应噪声抵消(Adaptive Noise Canceling,ANC)技术为抑制多个干扰提供了理论基础,但是求解稳态最佳滤波矩阵存在着技术实现上的困难。本文提出用一种反波束成形(Inverse Beamforming,IBF)递推算法,在阵元域逐一抵消多个强干扰,从而增强并提取出微弱目标信号。文中给出了递推求解由逆矩阵所表达的最佳滤波矢量的理论推导和相应的公式。利用IBF算法处理海试数据得到了较好的结果,显著改善了强干扰下对微弱信号的检测,甚至在普通波束成形(CBF)中未能显示出来的信号都可以被检测出来。      

波达方向估计中特征空间的信源数估计方法

提出了特征空间法信源数估计方法,它将阵列信号的协方差估计值分别投影到信号的特征子空间和噪声的特征子空间。由于信号子空间与噪声子空间相互正交,易于由表征投影大小的判据值区分信号和噪声的贡献;本方法用的是M×M阶矩阵特征值分解,M为基元数,与波达方向估计用的相同,因此节省大量的计算量;它可以在实数空间中进行运算,进一步减少运算量。进行了数值计算,检验了判据值分布,以及在信源等功率、不等功率和空间相关色噪声等情况下特征空间法的性能。估计方法还用声纳数据进行了检验。所有这些结果均证明本估计方法性能优良。      

Activation detection in event-related fMRI data based on spatio-temporal properties.

Template-based activation detection methods, such as cross-correlation, could be difficult to apply in event-related functional MRI data because accurate a priori knowledge about the activation signal patterns is often not available. As a result, several categories of template-free data analysis techniques have been introduced in the fMRI literature. One previously described template-free activation detection technique is based on the feature that activated voxels yield reproducible time course patterns as the subject undergoes the same simulation in repeated epochs. In this paper, spatial information is incorporated as a second feature and a combined univariate measure is formed. The resulting method is shown to offer measurable improvement in detecting activation regions in simulated data in a highly computationally efficient manner. Its practical utility is demonstrated with an experimental data set obtained with a visually guided motor paradigm.     

一种自适应最小范数算法

运用特征子空间方法的关键在于信号子空间或噪声子空间的估计,实际上有些信号的统计特性随时间变化,于是要求得到参数的实时估计值,为此,需要随时根据新的阵列接收数据对信号或噪声子空间进行更新。本文首先分析了一种自适应子空间估计算法,即MALASE(MaximumLikelihoodAdaptiveSubspaceEstimation)算法。然后,把MALASE算法与传统的最小范数(Mini-Norm)高分辨算法相结合,并应用零点跟踪技术,提出了一种自适应Mini-Norm高分辨算法,可用于对时变的信号波达方向(DOA)进行跟踪估计。计算机仿真结果验证了该算法的有效性。     

A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging

Granger causality model (GCM) derived from multivariate vector autoregressive models of data has been employed to identify effective connectivity in the human brain with functional magnetic resonance imaging (fMRI) and to reveal complex temporal and spatial dynamics underlying a variety of cognitive processes. In the most recent fMRI effective connectivity measures, pair-wise GCM has commonly been applied based on single-voxel values or average values from special brain areas at the group level. Although a few novel conditional GCM methods have been proposed to quantify the connections between brain areas, our study is the first to propose a viable standardized approach for group analysis of fMRI data with GCM. To compare the effectiveness of our approach with traditional pair-wise GCM models, we applied a well-established conditional GCM to preselected time series of brain regions resulting from general linear model (GLM) and group spatial kernel independent component analysis of an fMRI data set in the temporal domain. Data sets consisting of one task-related and one resting-state fMRI were used to investigate connections among brain areas with the conditional GCM method. With the GLM-detected brain activation regions in the emotion-related cortex during the block design paradigm, the conditional GCM method was proposed to study the causality of the habituation between the left amygdala and pregenual cingulate cortex during emotion processing. For the resting-state data set, it is possible to calculate not only the effective connectivity between networks but also the heterogeneity within a single network. Our results have further shown a particular interacting pattern of default mode network that can be characterized as both afferent and efferent influences on the medial prefrontal cortex and posterior cingulate cortex. These results suggest that the conditional GCM approach based on a linear multivariate vector autoregressive model can achieve greater accuracy in detecting network connectivity than the widely used pair-wise GCM, and this group analysis methodology can be quite useful to extend the information obtainable in fMRI.     

Principal component analysis for emergent acoustic signal detection with supporting simulation results

A method is introduced that uses principal component analysis (PCA) to detect emergent acoustic signals. Emergent signal detection is frequently used in radar applications to detect signals of interest in background clutter and in cognitive radio to detect the primary user in a frequency band. The method presented differs from other standard techniques in that the detection of the signal of interest is accomplished by detecting a change in the covariance between two channels of data instead of detecting the change in statistics of a single channel of data. For this paper, PCA is able to detect emergent acoustic signals by detecting when there is a change in the eigenvalue subspace of the covariance matrix caused by the addition of the signal of interest. The algorithm's performance is compared to an energy detector and the Neyman-Pearson theorem. Acoustic simulations were used to verify the performance of the algorithm. Simulations were also used to examine the effectiveness of the algorithm under various signal-to-interferer and signal-to-noise ratios, and using various test signals.