Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Analysis of functional networks involved in motor execution and motor imagery using combined hierarchical clustering analysis and independent component analysis

Cognitive experiments involving motor execution (ME) and motor imagery (MI) have been intensively studied using functional magnetic resonance imaging (fMRI). However, the functional networks of a multitask paradigm which include ME and MI were not widely explored. In this article, we aimed to investigate the functional networks involved in MI and ME using a method combining the hierarchical clustering analysis (HCA) and the independent component analysis (ICA). Ten right-handed subjects were recruited to participate a multitask experiment with conditions such as visual cue, MI, ME and rest. The results showed that four activation clusters were found including parts of the visual network, ME network, the MI network and parts of the resting state network. Furthermore, the integration among these functional networks was also revealed. The findings further demonstrated that the combined HCA with ICA approach was an effective method to analyze the fMRI data of multitasks.     

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.     

Preoperative localization of the sensorimotor area using independent component analysis of resting-state fMRI

Analysis of resting-state functional magnetic resonance imaging (fMRI) data is based on detecting low-frequency signal fluctuations in functionally connected brain areas. These synchronous fluctuations in resting-state networks have been observed in several studies with healthy subjects. In this study, we explored if independent component analysis (ICA) can be used to localize the sensorimotor area from resting-state fMRI data in patients with brain tumors. Finger-tapping activation task and resting-state blood-oxygenation-level-dependent fMRI data were acquired from 8 patients with brain tumors and 10 healthy volunteers. Sensorimotor task independent components (IC_task) were used to verify resting-state independent components (IC_rest) individually. In addition, sensorimotor IC_rests were compared between the groups and no significant differences were detected in volume, spatial correlation or temporal correlation. These results show that it is possible to localize a sensorimotor area from resting-state data using ICA in patients with brain tumors. This offers a complementary method for assessing the sensorimotor area in subjects with brain tumors who have difficulties in performing motor paradigms.     

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.     

Orthogonal-triangular decomposition ghost imaging

Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix $\bm Q$ and an upper triangular matrix $\bm R$. Then let the off-diagonal values of $\bm R$ equal to 0.0, the diagonal elements of $\bm R$ equal to a constant $k$, where $k$ is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.     

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.     

Respiratory noise correction using phase information

Respiratory noise is a confounding factor in functional magnetic resonance imaging (MRI) data analysis. A novel method called Respiratory noise Correction using Phase information is proposed to retrospectively correct for the respiratory noise in functional MRI (fMRI) time series. It is demonstrated that the respiratory movement and the phase of functional MRI images are highly correlated in time. The signal fluctuation due to respiratory movements can be effectively estimated from the phase variation and removed from the functional MRI time series using a Wiener filtering technique. In our experiments, this new method is compared with RETROICOR, which requires recording respiration signal simultaneously in an fMRI experiment. The two techniques show comparable performance with respect to the respiratory noise correction for fMRI time series. However, this technique is more advantageous because there is no need for monitoring the subjects’ respiration or changing functional MRI protocols. This technique is also potentially useful for correcting respiratory noise from abnormal breathing or when the respiration is not periodic.     

基于独立分量分析的高光谱图像压缩

在对原始数据进行虚拟维数估计的基础上,提出了一种基于最大距离端元提取+独立分量分析(Independent Component Analysis,ICA)的高光谱图像有损压缩方案.该方案首先应用最大距离端元抽取法提取高光谱数据各端元矢量,然后用快速独立分量分析生成独立分量,最后使用2维分层树集合分裂(Set Partitioning In Hierarchical Trees,SPIHT)算法对各独立分量图进行编码.计算机仿真结果证明,该算法在取得高压缩率的同时,能很好地保持数据的谱特征,是一种高效的三维数据压缩方法.