A variant of logistic transfer function in Infomax and a postprocessing procedure for independent component analysis applied to fMRI data

Independent component analysis with Infomax algorithm can separate functional magnetic resonance imaging (fMRI) data into independent spatial components (brain activation maps) and their associated time courses. In the current study, we propose a variant of the logistic transfer function in Infomax, referred to as a-logistic Infomax, and a postprocessing procedure to combine a consistently task-related (CTR) component with transiently task-related (TTR) components for a better definition of brain functional localization. This a-logistic Infomax introduced parameter a into the standard logistic transfer function of conventional Infomax algorithm. For postprocessing method, we suggest the use of a stepwise linear regression of CTR and TTR components to fit reference function and then to sum up with different weights only those with significant contributions to the reference function in order to obtain a task component activation map. The effectiveness of both approaches on separating components and functional localization was evaluated with simulated and real fMRI data.     

Validating the performance of one-time decomposition for fMRI analysis using ICA with automatic target generation process

Independent component analysis (ICA) has been proven to be effective for functional magnetic resonance imaging (fMRI) data analysis. However, ICA decomposition requires to optimize the unmixing matrix iteratively whose initial values are generated randomly. Thus the randomness of the initialization leads to different ICA decomposition results. Therefore, just one-time decomposition for fMRI data analysis is not usually reliable. Under this circumstance, several methods about repeated decompositions with ICA (RDICA) were proposed to reveal the stability of ICA decomposition. Although utilizing RDICA has achieved satisfying results in validating the performance of ICA decomposition, RDICA cost much computing time. To mitigate the problem, in this paper, we propose a method, named ATGP-ICA, to do the fMRI data analysis. This method generates fixed initial values with automatic target generation process (ATGP) instead of being produced randomly. We performed experimental tests on both hybrid data and fMRI data to indicate the effectiveness of the new method and made a performance comparison of the traditional one-time decomposition with ICA (ODICA), RDICA and ATGP-ICA. The proposed method demonstrated that it not only could eliminate the randomness of ICA decomposition, but also could save much computing time compared to RDICA. Furthermore, the ROC (Receiver Operating Characteristic) power analysis also denoted the better signal reconstruction performance of ATGP-ICA than that of RDICA.     

Independent component analysis in the presence of noise in fMRI

A noisy version of independent component analysis (noisy ICA) is applied to simulated and real functional magnetic resonance imaging (fMRI) data. The noise covariance is explicitly modeled by an autoregressive (AR) model of order 1. The unmixing matrix of the data is determined using a variant of the FastICA algorithm based on Gaussian moments. The sources are estimated using the principle of maximum likelihood by modeling the source densities as asymmetric exponential functions. Effect of dimensionality reduction on the effective noise covariance used, accuracy of the obtained mixing matrix and degree of improvement in estimating fMRI sources are investigated. The primary conclusions after using this method of evaluation are as follows: (a) weighting matrix estimates are similar for noisy and conventional ICA in the realm of typical fMRI data, and (b) source estimates are improved by 5% (as measured by the correlation coefficient) in realistic simulated data by explicitly modeling the source densities and the noise, even when just a simple white noise model is used.     

An independent component analysis-based approach on ballistocardiogram artifact removing

Interest about simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data acquisition has rapidly increased during the last years because of the possibility that the combined method offers to join temporal and spatial resolution, providing in this way a powerful tool to investigate spontaneous and evoked brain activities. However, several intrinsic features of MRI scanning become sources of artifacts on EEG data. Noise sources of a highly predictable nature such as those related to the pulse MRI sequence and those determined by magnetic gradient switching during scanning do not represent a major problem and can be easily removed. On the contrary, the ballistocardiogram (BCG) artifact, a large signal visible on all EEG traces and related to cardiac activity inside the magnetic field, is determined by sources that are not fully stereotyped and causing important limitations in the use of artifact-removing strategies. Recently, it has been proposed to use independent component analysis (ICA) to remove BCG artifact from EEG signals. ICA is a statistical algorithm that allows blind separation of statistically independent sources when the only available information is represented by their linear combination. An important drawback with most ICA algorithms is that they exhibit a stochastic behavior: each run yields slightly different results such that the reliability of the estimated sources is difficult to assess. In this preliminary report, we present a method based on running the FastICA algorithm many times with slightly different initial conditions. Clustering structure in the signal space of the obtained components provides us with a new way to assess the reliability of the estimated sources.     

Discussion on the choice of separated components in fMRI data analysis by spatial independent component analysis

By measuring the changes of magnetic resonance signals during a stimulation, the functional magnetic resonance imaging (fMRI) is able to localize the neural activation in the brain. In this report, we discuss the fMRI application of the spatial independent component analysis (spatial ICA), which maximizes statistical independence over spatial images. Included simulations show the possibility of the spatial ICA on discriminating asynchronous activations or different response patterns in an fMRI data set. An in vivo visual stimulation fMRI test was conducted, and the result shows a proper sum of the separated components as the final image is better than a single component, using fMRI data analysis by spatial ICA. Our result means that spatial ICA is a useful tool for the detection of different response activations and suggests that a proper sum of the separated independent components should be used for the imaging result of fMRI data processing.     

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.     

Derivative temporal clustering analysis: detecting prolonged neuronal activity

Temporal clustering analysis (TCA) and independent component analysis (ICA) are promising data-driven techniques in functional magnetic resonance imaging (fMRI) experiments to obtain brain activation maps in conditions with unknown temporal information regarding the neuronal activity. Although comparable to ICA in detecting transient neuronal activities, TCA fails to detect prolonged plateau brain activations. To eliminate this pitfall, a novel derivative TCA (DTCA) method was introduced and its algorithms with different subtraction intervals were tested on simulated data with a pattern of prolonged plateau brain activation. It was found that the best performance of DTCA method in generating functional maps could be obtained if the subtraction interval is equal to or larger than the length of the rising time of the fMRI response. The DTCA method and its theoretical predication were further investigated and validated using in vivo fMRI data sets. By removing the limitations in the previous TCA, DTCA has shown its powerful capability in detecting prolonged plateau neuronal activities.     

Optimizing ICA in fMRI using information on spatial regularities of the sources

Spatial independent component analysis (ICA) is a well-established technique for multivariate analysis of functional magnetic resonance imaging (fMRI) data. It blindly extracts spatiotemporal patterns of neural activity from functional measurements by seeking for sources that are maximally independent. Additional information on one or more sources (e.g., spatial regularity) is often available; however, it is not considered while looking for independent components. In the present work, we propose a new ICA algorithm based on the optimization of an objective function that accounts for both independence and other information on the sources or on the mixing model in a very general fashion. In particular, we apply this approach to fMRI data analysis and illustrate, by means of simulations, how inclusion of a spatial regularity term helps to recover the sources more effectively than with conventional ICA. The improvement is especially evident in high noise situations. Furthermore we employ the same approach on data sets from a complex mental imagery experiment, showing that consistency and physiological plausibility of relatively weak components are improved.     

Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Constrained independent component analysis (CICA) eliminates the order ambiguity of standard ICA by incorporating prior information into the learning process to sort the components intrinsically. However, the original CICA (OCICA) and its variants depend on a learning rate, which is not easy to be tuned for various applications. To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept. A complete stability analysis was provided for the proposed methods, which also made a correction to the stability analysis given to OCICA. Variations for adding constraints either to the components or to the associated time courses were derived too. Using synthetic data, the proposed methods yielded a better stability and a better source separation quality in terms of higher signal-to-noise-ratio and smaller performance index than OCICA. For the artificially generated brain activations, the new CICAs demonstrated a better sensitivity/specificity performance than standard univariate general linear model (GLM) and standard ICA. Original CICA showed a similar sensitivity/specificity gain but failed to converge for several times. Using functional magnetic resonance imaging (fMRI) data acquired with a well-characterized sensorimotor task, the proposed CICAs yielded better sensitivity than OCICA, standard ICA and GLM in all the target functional regions in terms of either higher t values or larger suprathreshold cluster extensions using the same significance threshold. In addition, they were more stable than OCICA and standard ICA for analyzing the sensorimotor fMRI data.     

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.     

基于独立成分分析的全波核磁共振信号噪声滤除方法研究

核磁共振测深(MRS)探水仪探测到的纳伏级微弱信号极易受到各种环境噪声的干扰, 严重影响信号特征参数的准确提取, 导致后续反演解释错误率增高. 针对这一难题, 提出了基于独立成分分析的快速固定点算法进行信噪分离. 首先分析了该算法用于全波MRS信号消噪的适用性; 其次, 采用数字正交法解决欠定盲源分离问题, 提出了频谱校正法实现分离信号幅值的有效恢复. 仿真结果表明, 该算法能够有效地实现全波MRS信号的信噪分离, 且数据拟合后初始振幅和弛豫时间的相对误差小于± 5.00%; 通过与其他经典算法的对比分析, 进一步证明了该算法消噪性能的优越性. 将该算法应用到野外实测信号处理, 结果证明其能有效滤除环境噪声.     

Iterative joint data detection and channel estimation for uplink MC-CDMA systems in the presence of frequency selective channels

This paper is concerned with joint multiuser detection and multichannel estimation (JDE) for uplink multicarrier code-division multiple-access (MC-CDMA) systems in the presence of frequency selective channels. The detection and estimation, implemented at the receiver, are based on a version of the expectation maximization (EM) algorithm and the space-alternating generalized expectation–maximization (SAGE) which are very suitable for multicarrier signal formats. The EM-JDE receiver updates the data bit sequences in parallel, while the SAGE-JDE receiver reestimates them successively. The channel parameters are updated in parallel in both schemes. Application of the EM-based algorithm to the problem of iterative data detection and channel estimation leads to a receiver structure that also incorporates a partial interference cancelation. Computer simulations show that the proposed algorithms have excellent BER end estimation performance.     

Cortex-based independent component analysis of fMRI time series

The cerebral cortex is the main target of analysis in many functional magnetic resonance imaging (fMRI) studies. Since only about 20% of the voxels of a typical fMRI data set lie within the cortex, statistical analysis can be restricted to the subset of the voxels obtained after cortex segmentation. While such restriction does not influence conventional univariate statistical tests, it may have a substantial effect on the performance of multivariate methods.

Here, we describe a novel approach for data-driven analysis of single-subject fMRI time series that combines techniques for the segmentation and reconstruction of the cortical surface of the brain and the spatial independent component analysis (sICA) of the functional time courses (TCs). We use the mesh of the white matter/gray matter boundary, automatically reconstructed from high-spatial-resolution anatomical MR images, to limit the sICA decomposition of a coregistered functional time series to those voxels which are within a specified region with respect to the cortical sheet (cortex-based ICA, or cbICA). We illustrate our analysis method in the context of fMRI blocked and event-related experimental designs and in an fMRI experiment with perceptually ambiguous stimulation, in which an a priori specification of the stimulation protocol is not possible.

A comparison between cbICA and conventional hypothesis-driven statistical methods shows that cortical surface maps and component TCs blindly obtained with cbICA reliably reflect task-related spatiotemporal activation patterns. Furthermore, the advantages of using cbICA when the specification of a temporal model of the expected hemodynamic response is not straightforward are illustrated and discussed. A comparison between cbICA and anatomically unconstrained ICA reveals that — beside reducing computational demand — the cortex-based approach improves the fitting of the ICA model in the gray matter voxels, the separation of cortical components and the estimation of their TCs, particularly in the case of fMRI data sets with a complex spatiotemporal statistical structure.     

Separating 4D multi-task fMRI data of multiple subjects by independent component analysis with projection

Independent component analysis (ICA) is a widely accepted method to extract brain networks underlying cognitive processes from functional magnetic resonance imaging (fMRI) data. However, the application of ICA to multi-task fMRI data is limited due to the potential non-independency between task-related components. The ICA with projection (ICAp) method proposed by our group (Hum Brain Mapp 2009;30:417–31) is demonstrated to be able to solve the interactions among task-related components for single subject fMRI data. However, it still must be determined if ICAp is capable of processing multi-task fMRI data over a group of subjects. Moreover, it is unclear whether ICAp can be reliably applied to event-related (ER) fMRI data. In this study, we combined the projection method with the temporal concatenation method reported by Calhoun (Hum Brain Mapp 2008;29:828–38), referred to as group ICAp, to perform the group analysis of multi-task fMRI data. Both a human fMRI rest data-based simulation and real fMRI experiments, of block design and ER design, verified the feasibility and reliability of group ICAp, as well as demonstrated that ICAp had the strength to separate 4D multi-task fMRI data into multiple brain networks engaged in each cognitive task and to adequately find the commonalities and differences among multiple tasks.     

A SVM-based quantitative fMRI method for resting-state functional network detection

Resting-state functional magnetic resonance imaging (fMRI) aims to measure baseline neuronal connectivity independent of specific functional tasks and to capture changes in the connectivity due to neurological diseases. Most existing network detection methods rely on a fixed threshold to identify functionally connected voxels under the resting state. Due to fMRI non-stationarity, the threshold cannot adapt to variation of data characteristics across sessions and subjects, and generates unreliable mapping results. In this study, a new method is presented for resting-state fMRI data analysis. Specifically, the resting-state network mapping is formulated as an outlier detection process that is implemented using one-class support vector machine (SVM). The results are refined by using a spatial-feature domain prototype selection method and two-class SVM reclassification. The final decision on each voxel is made by comparing its probabilities of functionally connected and unconnected instead of a threshold. Multiple features for resting-state analysis were extracted and examined using an SVM-based feature selection method, and the most representative features were identified. The proposed method was evaluated using synthetic and experimental fMRI data. A comparison study was also performed with independent component analysis (ICA) and correlation analysis. The experimental results show that the proposed method can provide comparable or better network detection performance than ICA and correlation analysis. The method is potentially applicable to various resting-state quantitative fMRI studies.     

基于子空间分析的人脸识别方法研究

人脸识别技术是模式识别和机器视觉领域的一个重要研究方向,在众多人脸识别的算法中,基于子空间分析的特征提取方法以其稳定可靠的识别效果成为了人脸识别中特征提取的主流方法之一。本文对目前应用较多的子空间分析方法进行了研究,具体介绍了线性子空间分析方法：主成分分析（PCA）、线性鉴别分析（LDA）、独立主成分分析（ICA）、快速主成分分析（FastICA）等及非线性子空间分析方法：基于核的PCA （KPCA）等的基本思想及其在人脸识别中的研究进展,包括一些新的研究成果。此外,还应用orl及Yale B人脸库对几个基础的子空间方法进行了验证实验。实验结果表明,在几个子空间分析方法中,FastICA算法取得了最高的识别率。最后结合实验结果对各算法的优缺点进行了分析总结。     

Controlling the false positive rate in fuzzy clustering using randomization: application to fMRI activation detection

Despite its potential advantages for fMRI analysis, fuzzy C-means (FCM) clustering suffers from limitations such as the need for a priori knowledge of the number of clusters, and unknown statistical significance and instability of the results. We propose a randomization-based method to control the false-positive rate and estimate statistical significance of the FCM results. Using this novel approach, we develop an fMRI activation detection method. The ability of the method in controlling the false-positive rate is shown by analysis of false positives in activation maps of resting-state fMRI data. Controlling the false-positive rate in FCM allows comparison of different fuzzy clustering methods, using different feature spaces, to other fMRI detection methods. In this article, using simulation and real fMRI data, we compare a novel feature space that takes the variability of the hemodynamic response function into account (HRF-based feature space) to the conventional cross-correlation analysis and FCM using the cross-correlation feature space. In both cases, the HRF-based feature space provides a greater sensitivity compared to the cross-correlation feature space and conventional cross-correlation analysis. Application of the proposed method to finger-tapping fMRI data, using HRF-based feature space, detected activation in sub-cortical regions, whereas both of the FCM with cross-correlation feature space and the conventional cross-correlation method failed to detect them.     

Realignment strategies for awake-monkey fMRI data

Functional magnetic resonance imaging (fMRI) experiments with awake nonhuman primates (NHPs) have recently seen a surge of applications. However, the standard fMRI analysis tools designed for human experiments are not optimal for NHP data collected at high fields. One major difference is the experimental setup. Although real head movement is impossible for NHPs, MRI image series often contain visible motion artifacts. Animal body movement results in image position changes and geometric distortions. Since conventional realignment methods are not appropriate to address such differences, algorithms tailored specifically for animal scanning become essential. We have implemented a series of high-field NHP specific methods in a software toolbox, fMRI Sandbox (http://kyb.tuebingen.mpg.de/~stoewer/), which allows us to use different realignment strategies. Here we demonstrate the effect of different realignment strategies on the analysis of awake-monkey fMRI data acquired at high field (7 T). We show that the advantage of using a nonstandard realignment algorithm depends on the amount of distortion in the dataset. While the benefits for less distorted datasets are minor, the improvement of statistical maps for heavily distorted datasets is significant.     

Strategies for reducing large fMRI data sets for independent component analysis

In independent component analysis (ICA), principal component analysis (PCA) is generally used to reduce the raw data to a few principal components (PCs) through eigenvector decomposition (EVD) on the data covariance matrix. Although this works for spatial ICA (sICA) on moderately sized fMRI data, it is intractable for temporal ICA (tICA), since typical fMRI data have a high spatial dimension, resulting in an unmanageable data covariance matrix. To solve this problem, two practical data reduction methods are presented in this paper. The first solution is to calculate the PCs of tICA from the PCs of sICA. This approach works well for moderately sized fMRI data; however, it is highly computationally intensive, even intractable, when the number of scans increases. The second solution proposed is to perform PCA decomposition via a cascade recursive least squared (CRLS) network, which provides a uniform data reduction solution for both sICA and tICA. Without the need to calculate the covariance matrix, CRLS extracts PCs directly from the raw data, and the PC extraction can be terminated after computing an arbitrary number of PCs without the need to estimate the whole set of PCs. Moreover, when the whole data set becomes too large to be loaded into the machine memory, CRLS-PCA can save data retrieval time by reading the data once, while the conventional PCA requires numerous data retrieval steps for both covariance matrix calculation and PC extractions. Real fMRI data were used to evaluate the PC extraction precision, computational expense, and memory usage of the presented methods.     

Combining independent component analysis and correlation analysis to probe interregional connectivity in fMRI task activation datasets

A new approach in studying interregional functional connectivity using functional magnetic resonance imaging (fMRI) is presented. Functional connectivity may be detected by means of cross correlating time course data from functionally related brain regions. These data exhibit high temporal coherence of low frequency fluctuations due to synchronized blood flow changes. In the past, this fMRI technique for studying functional connectivity has been applied to subjects that performed no prescribed task ("resting" state). This paper presents the results of applying the same method to task-related activation datasets. Functional connectivity analysis is first performed in areas not involved with the task. Then a method is devised to remove the effects of activation from the data using independent component analysis (ICA) and functional connectivity analysis is repeated. Functional connectivity, which is demonstrated in the "resting brain," is not affected by tasks which activate unrelated brain regions. In addition, ICA effectively removes activation from the data and may allow us to study functional connectivity even in the activated regions.