Study of temporal stationarity and spatial consistency of fMRI noise using independent component analysis

Spatial independent component analysis (ICA) was used to study the temporal stationarity and spatial consistency of structured functional MRI (fMRI) noise. Spatial correlations have been used in the past to generate filters for the removal of structured noise for each time-course in an fMRI dataset. It would be beneficial to produce a multivariate filter based on the same principles. ICA is examined to determine if it has properties that are beneficial for this type of filtering. Six fMRI baseline datasets were decomposed via spatial ICA. The time-courses associated with each component were tested for wide-sense stationarity using the wide sense stationarity quotient (WSS). Each dataset was divided into three subsets and each subset was decomposed. The components of first and third subset were matched by the strength of their correlation. The components produced by ICA were found to have largely nonstationary time-courses. Despite the temporal nonstationarity in the data, ICA was found to produce consistent spatial components. The degree of correlation among components differed depending on the amount of dimension reduction performed on the data. It was found that a relatively small number of dimensions produced components that are potentially useful for generating a spatial fMRI filter.     

Automatic classification of brain resting states using fMRI temporal signals

A novel technique is presented for the automatic discrimination between networks of `resting states? of the human brain and physiological fluctuations in functional magnetic resonance imaging (fMRI). The method is based on features identified via a statistical approach to group independent component analysis time courses, which may be extracted from fMRI data. This technique is entirely automatic and, unlike other approaches, uses temporal rather than spatial information. The method achieves 83% accuracy in the identification of resting state networks.     

Independent Component Analysis Applied to fMRI Data: A Generative Model for Validating Results

Methods for testing and validating independent component analysis (ICA) results in fMRI are growing in importance as the popularity of this model for studying brain function increases. We introduce and apply a synthesis/analysis model for analyzing functional Magnetic Resonance Imaging (fMRI) data using ICA. Classes of signal types relevant to fMRI are described and a statistical approach for validation of simulation results is developed. Additionally, we propose an empirical version of our validation approach to test the performance of various ICA approaches in “hybrid” fMRI data, a mixture of real fMRI data and known (validatable) sources. The synthesis portion of the model assumes statistically independent spatial sources in the brain. We also assume that the fMRI scanner acquires overdetermined data such that there are more time points than hemodynamic brain sources. We propose several signal classes relevant to fMRI and discuss the properties of each. The analysis portion of the model includes several candidates for spatial smoothing, ICA algorithm, and data reduction. We use the Kullback-Leibler divergence between the estimated source distributions and the “true” distributions as a measure of the optimality of the final ICA decomposition. Using this model, we generate fMRI-like data and optimize the analysis stage as a function of ICA algorithm, data reduction scheme, and spatial smoothing. An example of how our synthesis/analysis model can be used in validating an fMRI experiment is demonstrated using simulations and “hybrid” fMRI data.     

Effect of spatial alignment transformations in PCA and ICA of functional neuroimages

It has been previously observed that independent component analysis (ICA), if applied to data pooled in a particular way, may lessen the need for spatial alignment of scans in a functional neuroimaging study. In this paper, we seek to determine analytically the conditions under which this observation is true, not only for spatial ICA, but also for temporal ICA and for principal component analysis (PCA). In each case, we find conditions that the spatial alignment operator must satisfy to ensure invariance of the results. We illustrate our findings using functional magnetic-resonance imaging (fMRI) data. Our analysis is applicable to both intersubject and intrasubject spatial normalization.     

Analysis of fMRI data using improved self-organizing mapping and spatio-temporal metric hierarchical clustering

The self-organizing mapping (SOM) and hierarchical clustering (HC) methods are integrated to detect brain functional activation; functional magnetic resonance imaging (fMRI) data are first processed by SOM to obtain a primary merged neural nodes image, and then by HC to obtain further brain activation patterns. The conventional Euclidean distance metric was replaced by the correlation distance metric in SOM to improve clustering and merging of neural nodes. To improve the use of spatial and temporal information in fMRI data, a new spatial distance (node coordinates in the 2-D lattice) and temporal correlation (correlation degree of each time course in the exemplar matrix) are introduced in HC to merge the primary SOM results. Two simulation studies and two in vivo fMRI data that both contained block-design and event-related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods. Our results demonstrate that the improved SOM and HC methods are clearly superior to the statistical parametric mapping (SPM), independent component analysis (ICA), and conventional SOM methods in the block-design, especially in the event-related experiment, as revealed by their performance measured by receiver operating characteristic (ROC) analysis. Our results also suggest that the proposed new integrated approach could be useful in detecting block-design and event-related fMRI data.      

An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis

A three-dimensional image registration method for motion correction of functional magnetic resonance imaging (fMRI) time-series, based on independent component analysis (ICA), is described. We argue that movement during fMRI data acquisition results in a simultaneous increase in the joint entropy of the observed time-series and a decrease in the joint entropy of a nonlinear function of the derived spatially independent components calculated by ICA. We propose this entropy difference as a reliable criterion for motion correction and refer to a method that maximizes this as motion-corrected ICA (MCICA). Specifically, a given motion-corrupted volume may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion. In essence, MCICA consists of designing an adaptive spatial resampling filter which maintains maximum temporal independence among the recovered components. In contrast with conventional registration methods, MCICA does not require registration of motion-corrupted volumes to a single reference volume which can introduce artifacts because corrections are applied without accounting for variability due to the task-related activation. Simulations demonstrate that MCICA is robust to activation level, additive noise, random motion in the reference volumes and the exact number of independent components extracted. When the method was applied to real data with minimal estimated motion, the method had little effect and, hence, did not introduce spurious changes in the data. However, in a data series from a motor fMRI experiment with larger motion, preprocessing the data with the proposed method resulted in the emergence of activation in primary motor and supplementary motor cortices. Although mutual information (MI) was not explicitly optimized, the MI between all subsequent volumes and the first one was consistently increased for all volumes after preprocessing the data with MCICA. We suggest MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion.     

基于fMRI功能网络和贝叶斯矩阵分解的脑电源成像方法

脑电(EEG)是一种重要的脑功能成像技术,根据头皮记录的EEG信号重构皮层脑活动称为EEG源成像。然而脑源活动位置和尺寸的准确重构依然是一个挑战。为充分利用EEG和功能磁共振(fMRI)信号在时空分辨率上的互补信息,该文提出一个新的源成像方法——基于fMRI脑网络和时空约束的EEG源重构算法(FN-STCSI)。该方法在参数贝叶斯框架下,基于矩阵分解思想将源信号分解为若干时间基函数的线性组合。此外,为融合fMRI的高空间分辨率信息,FN-STCSI利用独立成分分析提取fMRI信号的功能网络,构建EEG源成像的空间协方差基,通过变分贝叶斯推断技术确定每个空间协方差基的相对贡献,实现EEG-fMRI融合。通过蒙特卡罗数值仿真和实验数据分析比较了FN-STCSI与现有算法在不同信噪比和不同先验条件下的性能,结果表明FN-STCSI能有效融合EEG-fMRI在时空上的互补信息,提高EEG弥散源成像的性能。     

Comparison of two exploratory data analysis methods for fMRI: unsupervised clustering versus independent component analysis

Exploratory data-driven methods such as unsupervised clustering and independent component analysis (ICA) are considered to be hypothesis-generating procedures, and are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). In this paper, we present a comparison between unsupervised clustering and ICA in a systematic fMRI study. The comparative results were evaluated by 1) task-related activation maps, 2) associated time-courses, and 3) receiver operating characteristic analysis. For the fMRI data, a comparative quantitative evaluation between the three clustering techniques, self-organizing map, "neural gas" network, and fuzzy clustering based on deterministic annealing, and the three ICA methods, FastICA, Infomax and topographic ICA was performed. The ICA methods proved to extract features relatively well for a small number of independent components but are limited to the linear mixture assumption. The unsupervised Clustering outperforms ICA in terms of classification results but requires a longer processing time than the ICA methods.     

Group replicator dynamics: a novel group-wise evolutionary approach for sparse brain network detection

Functional magnetic resonance imaging (fMRI) is increasingly used for studying functional integration of the brain. However, large inter-subject variability in functional connectivity, particularly in disease populations, renders detection of representative group networks challenging. In this paper, we propose a novel technique, "group replicator dynamics" (GRD), for detecting sparse functional brain networks that are common across a group of subjects. We extend the replicator dynamics (RD) approach, which we show to be a solution of the nonnegative sparse principal component analysis problem, by integrating group information into each subject's RD process. Our proposed strategy effectively coaxes all subjects' networks to evolve towards the common network of the group. This results in sparse networks comprising the same brain regions across subjects yet with subject-specific weightings of the identified brain regions. Thus, in contrast to traditional averaging approaches, GRD enables inter-subject variability to be modeled, which facilitates statistical group inference. Quantitative validation of GRD on synthetic data demonstrated superior network detection performance over standard methods. When applied to real fMRI data, GRD detected task-specific networks that conform well to prior neuroscience knowledge.     

MICA: a multilinear ICA decomposition for natural scene modeling.

We refine the classical independent component analysis (ICA) decomposition using a multilinear expansion of the probability density function of the source statistics. In particular, we introduce a specific nonlinear system that allows us to elegantly capture the statistical dependences between the responses of the multilinear ICA (MICA) filters. The resulting multilinear probability density is analytically tractable and does not require Monte Carlo simulations to estimate the model parameters. We demonstrate the MICA model on natural image textures and envision that the new model will prove useful for analyzing nonstationarity natural images using natural scene statistics models.     

Temporally constrained ICA: an application to artifact rejection in electromagnetic brain signal analysis

Independent component analysis (ICA) is a technique which extracts statistically independent components from a set of measured signals. The technique enjoys numerous applications in biomedical signal analysis in the literature, especially in the analysis of electromagnetic (EM) brain signals. Standard implementations of ICA are restrictive mainly due to the square mixing assumption-for signal recordings which have large numbers of channels, the large number of resulting extracted sources makes the subsequent analysis laborious and highly subjective. There are many instances in neurophysiological analysis where there is strong a priori information about the signals being sought; temporally constrained ICA (cICA) can extract signals that are statistically independent, yet which are constrained to be similar to some reference signal which can incorporate such a priori information. We demonstrate this method on a synthetic dataset and on a number of artifactual waveforms identified in multichannel recordings of EEG and MEG. cICA repeatedly converges to the desired component within a few iterations and subjective analysis shows the waveforms to be of the expected morphologies and with realistic spatial distributions. This paper shows that cICA can be applied with great success to EM brain signal analysis, with an initial application in automating artifact extraction in EEG and MEG.     

Order Selection of the Linear Mixing Model for Complex-Valued FMRI Data

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA). In this work, we develop a complex-valued order selection method to estimate the dimension of signal subspace using information-theoretic criteria. To correct the effect of sample dependence to information-theoretic criteria, we develop a general entropy rate measure for complex Gaussian random process to calibrate the independent and identically distributed (i.i.d.) sampling scheme in the complex domain. We show the effectiveness of the approach for order selection on both simulated and actual fMRI data. A comparison between the results of order selection and ICA on real-valued and complex-valued fMRI data demonstrates that a fully complex analysis extracts more meaningful components about brain activation.     

Two Dimensional Spatial Independent Component Analysis and Its Application in fMRI Data Process

One important application of independent component analysis （ICA） is in image processing. A two dimensional （2-D） composite ICA algorithm framework for 2-D image independent component analysis （2-D ICA） is proposed. The 2-D nature of the algorithm provides it an advantage of circumventing the roundabout transforming procedures between two dimensional （2-D） image deta and one-dimensional （l-D） signal. Moreover the combination of the Newton （fixed-point algorithm） and natural gradient algorithms in this composite algorithm increases its efficiency and robustness. The convincing results of a successful example in functional magnetic resonance imaging （fMRI） show the potential application of composite 2-D ICA in the brain activity detection.     

Variational Bayes inference of spatial mixture models for segmentation

Mixture models are commonly used in the statistical segmentation of images. For example, they can be used for the segmentation of structural medical images into different matter types, or of statistical parametric maps into activating and nonactivating brain regions in functional imaging. Spatial mixture models have been developed to augment histogram information with spatial regularization using Markov random fields (MRFs). In previous work, an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization. Inference was performed using Markov Chain Monte Carlo (MCMC) sampling. However, this approach is prohibitively slow for large datasets. In this work, a more efficient inference approach is presented. This combines a variational Bayes approximation with a second-order Taylor expansion of the components of the posterior distribution, which would otherwise be intractable to Variational Bayes. This provides inference on fully adaptive spatial mixture models an order of magnitude faster than MCMC. We examine the behavior of this approach when applied to artificial data with different spatial characteristics, and to functional magnetic resonance imaging statistical parametric maps.     

Application of independent component analysis with adaptive density model to complex-valued fMRI data

Independent component analysis (ICA) has proven quite useful for the analysis of real world datasets such as functional resonance magnetic imaging (fMRI) data, where the underlying nature of the data is hard to model. It is particularly useful for the analysis of fMRI data in its native complex form since very little is known about the nature of phase. Phase information has been discarded in most analyses as it is particularly noisy. In this paper, we show that a complex ICA approach using a flexible nonlinearity that adapts to the source density is the more desirable one for performing ICA of complex fMRI data compared to those that use fixed nonlinearity, especially when noise level is high. By adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of spatial maps and the task-related time courses, especially for the estimation of phase of the time course. We also define a procedure for analysis and visualization of complex-valued fMRI results, which includes the construction of bivariate t-maps for multiple subjects and a complex-valued ICASSO scheme for evaluating the consistency of ICA algorithms.     

Uncorrelated component analysis for blind source separation

The uncorrelated component analysis (UCA) of a stationary random vector process consists of searching for a linear transformation that minimizes the temporal correlation between its components. Through a general analysis we show that under practically reasonable and mild conditions UCA is a solution for blind source separation. The theorems proposed in this paper for UCA provide useful insights for developing practical algorithms. UCA explores the temporal information of the signals, whereas independent component analysis (ICA) explores the spatial information; thus UCA can be applied for source separation in some cases where ICA cannot. For blind source separation, combining ICA and UCA may give improved performance because more information can be utilized. The concept of single UCA (SUCA) is also proposed, which leads to sequential source separation.This work was supported in part by grants from the Research Grants Council of Hong Kong, grants HKU553/96M, HKU7036/97E, and HKUST776/96E.     

时间独立分量分析模型的新息方法

考虑时间独立分量分析(TICA)模型中的时间结构信息,引入新息思想,提出TICA的新息模型和估计方法(ITICA)。研究表明：1)TICA的新息模型仍然满足经典独立分量分析(ICA)的潜在分量统计独立和非高斯假设,TICA模型中的混合矩阵(或分离矩阵)可以从对应的ITICA模型中估计得到；2)随着新息的引入,新模型中的潜在独立分量非高斯性增强,ITICA方法能有效提高估计的效率。实验结果表明,ITICA方法可以改善经典ICA算法的收敛性,解决实际中近似独立源信号估计过程中出现的收敛振荡和速度慢的问题,结合先验知识和选择合适的新息还可以有效提高算法的辨识精度。     

Interconnect crosstalk noise evaluation in deep-submicron technologies

To solve the crosstalk noise problem in deep-submicron technologies, a statistical method for analyzing crosstalk noise with reduced distributed RC-π model is proposed in this paper. First, quiet aggressor net and tree branch reduction techniques are introduced into the distributed RC-π model, and a new spatial correlation model for both Gaussian and non-Gaussian process variations among segments is created. Then, principal components analysis (PCA) and independent component analysis (ICA) techniques are applied to reduce correlations of process variations. Finally, the moment matching scheme is used to obtain the probability density function (PDF) of crosstalk noise in victim coupled with multiple aggressors. Experimental results show that our method maintains the efficiency of previous approaches, and significantly improves on their accuracy.     

Electrophysiological imaging of brain activity and connectivity-challenges and opportunities

Unlocking the dynamic inner workings of the brain continues to remain a grand challenge of the 21st century. To this end, functional neuroimaging modalities represent an outstanding approach to better understand the mechanisms of both normal and abnormal brain functions. The ability to image brain function with ever increasing spatial and temporal resolution has made a significant leap over the past several decades. Further delineation of functional networks could lead to improved understanding of brain function in both normal and diseased states. This paper reviews recent advancements and current challenges in dynamic functional neuroimaging techniques, including electrophysiological source imaging, multimodal neuroimaging integrating fMRI with EEG/MEG, and functional connectivity imaging.