Joint Blind Source Separation by Multiset Canonical Correlation Analysis

In this paper, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multiset canonical correlation analysis (M-CCA) [J. R. Kettenring, "Canonical analysis of several sets of variables", Biometrika, vol. 58, pp. 433-451, 1971]. We first propose a generative model of joint BSS based on the correlation of latent sources within and between datasets. We specify source separability conditions, and show that, when the conditions are satisfied, the group of corresponding sources from each dataset can be jointly extracted by M-CCA through maximization of correlation among the extracted sources. We compare source separation performance of the M-CCA scheme with other joint BSS methods and demonstrate the superior performance of the M-CCA scheme in achieving joint BSS for a large number of datasets, group of corresponding sources with heterogeneous correlation values, and complex-valued sources with circular and non-circular distributions. We apply M-CCA to analysis of functional magnetic resonance imaging (fMRI) data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task.     

Statistical maps for EEG dipolar source localization

We present a method that estimates three-dimensional statistical maps for electroencephalogram (EEG) source localization. The maps assess the likelihood that a point in the brain contains a dipolar source, under the hypothesis of one, two or three activated sources. This is achieved by examining all combinations of one to three dipoles on a coarse grid and attributing to each combination a score based on an F statistic. The probability density function of the statistic under the null hypothesis is estimated nonparametrically, using bootstrap resampling. A theoretical F distribution is then fitted to the empirical distribution in order to allow correction for multiple comparisons. The maps allow for the systematic exploration of the solution space for dipolar sources. They permit to test whether the data support a given solution. They do not rely on the assumption of uncorrelated source time courses. They can be compared to other statistical parametric maps such as those used in functional magnetic resonance imaging (fMRI). Results are presented for both simulated and real data. The maps were compared with LORETA and MUSIC results. For the real data consisting of an average of epileptic spikes, we observed good agreement between the EEG statistical maps, intracranial EEG recordings, and fMRI activations.     

Automatic identification of functional clusters in FMRI data using spatial dependence

In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.     

Elastic registration of fMRI data using Bézier-spline transformations

A three-dimensional (3-D) elastic registration algorithm has been developed to find a veridical transformation that maps activation patterns from functional magnetic resonance imaging (fMRI) experiments onto a 3-D high-resolution anatomical dataset. The proposed algorithm uses trilinear Bézier-splines and a 3-D voxel-based optimization technique to determine the transformation that maps the functional data onto the coordinate system of the anatomical dataset. Simple conditions are presented which guarantee that the data are mapped one-to-one on each other. Two voxel-based similarity measures, the linear correlation coefficient and the entropy correlation coefficient, are used. Their performance with respect to the registration of fMRI data is compared. Tests on simulated and real data have been performed to evaluate the accuracy of the method. Our results demonstrate that subvoxel accuracy can be achieved even for noisy low-resolution multislice datasets with local distortions up to 10 mm. Although the method is optimized for the registration of functional and anatomical MR images, it can also be used for solving other elastic registration problems.     

Simultaneous registration and activation detection for fMRI

Registration using the least-squares cost function is sensitive to the intensity fluctuations caused by the blood oxygen level dependent (BOLD) signal in functional MRI (fMRI) experiments, resulting in stimulus-correlated motion errors. These errors are severe enough to cause false-positive clusters in the activation maps of datasets acquired from 3T scanners. This paper presents a new approach to resolving the coupling between registration and activation. Instead of treating the two problems as individual steps in a sequence, they are combined into a single least-squares problem and are solved simultaneously. Robustness tests on a variety of simulated three-dimensional EPI datasets show that the stimulus-correlated motion errors are removed, resulting in a substantial decrease in false-positive and false-negative activation rates. The new method is also shown to decorrelate the motion estimates from the stimulus by testing it on different in vivo fMRI datasets acquired from two different 3T scanners.     

Joint Detection-Estimation of Brain Activity in Functional MRI: A Multichannel Deconvolution Solution

Analysis of functional magnetic resonance imaging (fMRI) data focuses essentially on two questions: first, a detection problem that studies which parts of the brain are activated by a given stimulus and, second, an estimation problem that investigates the temporal dynamic of the brain response during activations. Up to now, these questions have been addressed independently. However, the activated areas need to be known prior to the analysis of the temporal dynamic of the response. Similarly, a typical shape of the response has to be assumed a priori for detection purpose. This situation motivates the need for new methods in neuroimaging data analysis that are able to go beyond this unsatisfactory tradeoff. The present paper raises a novel detection-estimation approach to perform these two tasks simultaneously in region-based analysis. In the Bayesian framework, the detection of brain activity is achieved using a mixture of two Gaussian distributions as a prior model on the “neural” response levels, whereas the hemodynamic impulse response is constrained to be smooth enough in the time domain with a Gaussian prior. All parameters of interest, as well as hyperparameters, are estimated from the posterior distribution using Gibbs sampling and posterior mean estimates. Results obtained both on simulated and real fMRI data demonstrate first that our approach can segregate activated and nonactivated voxels in a given region of interest (ROI) and, second, that it can provide spatial activation maps without any assumption on the exact shape of the Hemodynamic Response Function (HRF), in contrast to standard model-based analysis.     

An integrated neighborhood correlation and hierarchical clustering approach of functional MRI

Clustering analysis is a promising data-driven method for the analysis of functional magnetic resonance imaging (fMRI) time series, however, the huge computation load makes it difficult for practical use. In this paper, neighborhood correlation (NC) and hierarchical clustering (HC) methods are integrated as a new approach where fMRI data are processed first by NC to get a preliminary image of brain activations, and then by HC to remove some noises. In HC, to better use spatial and temporal information in fMRI data, a new spatio-temporal measure is introduced. A simulation study and an application to visual fMRI data show that the brain activations can be effectively detected and that different response patterns can be discriminated. These results suggest that the proposed new integrated approach could be useful in detecting weak fMRI signals.     

Modeling brain activation in fMRI using group MRF

Noise confounds present serious complications to functional magnetic resonance imaging (fMRI) analysis. The amount of discernible signals within a single dataset of a subject is often inadequate to obtain satisfactory intra-subject activation detection. To remedy this limitation, we propose a novel group Markov random field (GMRF) that extends each subject's neighborhood system to other subjects to enable information coalescing. A distinct advantage of GMRF over standard fMRI group analysis is that no stringent one-to-one voxel correspondence is required. Instead, intra- and inter-subject neighboring voxels are jointly regularized to encourage spatially proximal voxels to be assigned similar labels across subjects. Our proposed group-extended graph structure thus provides an effective means for handling inter-subject variability. Also, adopting a group-wise approach by integrating group information into intra-subject activation, as opposed to estimating a single average group map, permits inter-subject differences to be characterized and studied. GMRF can be elegantly implemented as a single MRF, thus enabling all subjects' activation maps to be simultaneously and collaboratively segmented with global optimality guaranteed in the case of binary labeling. We validate our technique on synthetic and real fMRI data and demonstrate GMRF's superior performance over standard fMRI analysis.     

Unsupervised robust nonparametric estimation of the hemodynamic response function for any fMRI experiment

This paper deals with the estimation of the blood oxygen level-dependent response to a stimulus, as measured in functional magnetic resonance imaging (fMRI) data. A precise estimation is essential for a better understanding of cerebral activations. The most recent works have used a nonparametric framework for this estimation, considering each brain region as a system characterized by its impulse response, the so-called hemodynamic response function (HRF). However, the use of these techniques has remained limited since they are not well-adapted to real fMRI data. Here, we develop a threefold extension to previous works. We consider asynchronous event-related paradigms, account for different trial types and integrate several fMRI sessions into the estimation. These generalizations are simultaneously addressed through a badly conditioned observation model. Bayesian formalism is used to model temporal prior information of the underlying physiological process of the brain hemodynamic response. By this way, the HRF estimate results from a tradeoff between information brought by the data and by our prior knowledge. This tradeoff is modeled with hyperparameters that are set to the maximum-likelihood estimate using an expectation conditional maximization algorithm. The proposed unsupervised approach is validated on both synthetic and real fMRI data, the latter originating from a speech perception experiment.     

Estimation of the hemodynamic response of fMRI Data using RBF neural network

Functional magnetic resonance imaging (fMRI) is an important technique for neuroimaging. The conventional system identification methods used in fMRI data analysis assume a linear time-invariant system with the impulse response described by the hemodynamic responses (HDR). However, the measured blood oxygenation level-dependent (BOLD) signals to a particular processing task (for example, rapid event-related fMRI design) show nonlinear properties and vary with different brain regions and subjects. In this paper, radial basis function (RBF) neural network (a powerful technique for modelling nonlinearities) is proposed to model the dynamics underlying the fMRI data. The equivalence of the proposed method to the existing Volterra series method has been demonstrated. It is shown that the first- and second-order Volterra kernels could be deduced from the parameters of the RBF neural network. Studies on both simulated (using Balloon model) as well as real event-related fMRI data show that the proposed method can accurately estimate the HDR of the brain and capture the variations of the HDRs as a function of the brain regions and subjects.     

融合先验信息的脑功能图像分割

基于静息态功能磁共振图像(fMRI)的脑功能区分割广泛采用K均值聚类和谱聚类等无监督聚类算法。但这些算法对图像噪声较为敏感,可能会产生不可靠的脑区分割结果。文中提出了一种融合先验信息的半监督聚类算法,可以可靠地确定各子区间的边界,从而得到稳定的分割结果。提出的方法对人类右侧大脑的Broca区(BA44/45区)进行分割验证,实验结果表明,文中的方法不仅得到了可靠的功能子区边界,而且获得了较高的个体间一致性。     

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.     

Structural group classification technique based on regional fMRI BOLD responses

This paper presents a new multigroup classification method based on subtle differences in regional brain activity during the completion of a functional magnetic resonance imaging (fMRI) challenge paradigm. Classification is performed based on features derived from BOLD time intensity curves in selected regions of interest (ROI). For each ROI, a mean time intensity curve [called mean regional response (MRR)] is calculated from realigned and normalized datasets. The overall subject performance is characterized with a vector of features obtained using nonlinear modeling of all subject's MRRs with a mixture of time shifted Gaussian functions. The classification is performed in the reduced-dimension optimal discrimination space, obtained through canonical transformations of original feature space. In order to demonstrate feasibility of the proposed method, classification of three groups of subjects is presented. The three groups are defined as heavy marijuana smokers after 24 hours of abstinence, heavy marijuana smokers after 28 days of abstinence, and healthy nonusing controls. The proposed method can be useful as an analytic tool for the discrimination of different groups of subjects based on temporal features of functional magnetic resonance imaging activation.     

Characterization of dynamic 3-D PET imaging for functional brainmapping

Methods for optimizing the acquisition, reconstruction and analysis of positron emission tomography (PET) images for functional brain mapping have been investigated. The scatter fraction and noise-equivalent count rate characteristics were measured for the ECAT 951/31R PET scanner operating in septa-extended two-dimensional (2-D) and septa-retracted three-dimensional (3-D) modes. The 3-D mode is shown to provide higher signal-to-noise images than the 2-D mode at specific activities less than 30 kBq/ml. To enable increased temporal resolution in dynamic 3-D PET activation studies, a parallel version of the 3-D reconstruction algorithm was developed. Implementation of the reprojection algorithm on an 88 processor i860 supercomputer resulted in a more than tenfold increase in reconstruction speed compared to a single i860 processor system. An investigation of the optimal duration for imaging brain activations was undertaken in 12 normal subjects using repeated H₂¹⁵O slow infusions and a visually presented lexical decision task. The significance of change in regional cerebral blood flow (CBF) was determined using statistical parametric maps for images acquired during stimulation, immediately after stimulation, and commencing 1 min after cessation of the stimulus. Regions of CBF change were detected in all three images. Dynamic 3-D, or four-dimensional (4-D), PET activation scanning is shown to be practical and likely to further improve the sensitivity of PET for detection of subtle regional CBF changes in functional brain mapping research     

Analysis of FMRI data using an integrated principal component analysis and supervised affinity propagation clustering approach

Clustering analysis is a promising data-driven method for analyzing functional magnetic resonance imaging (fMRI) time series data. The huge computational load, however, creates practical difficulties for this technique. We present a novel approach, integrating principal component analysis (PCA) and supervised affinity propagation clustering (SAPC). In this method, fMRI data are initially processed by PCA to obtain a preliminary image of brain activation. SAPC is then used to detect different brain functional activation patterns. We used a supervised Silhouette index to optimize clustering quality and automatically search for the optimal parameter p in SAPC, so that the basic affinity propagation clustering is improved by applying SAPC. Four simulation studies and tests with three in vivo fMRI datasets containing data from both block-design and event-related experiments revealed that functional brain activation was effectively detected and different response patterns were distinguished using our integrated method. In addition, the improved SAPC method was superior to the k -centers clustering and hierarchical clustering methods in both block-design and event-related fMRI data, as measured by the average squared error. These results suggest that our proposed novel integrated approach will be useful for detecting brain functional activation in both block-design and event-related experimental fMRI data.     

Estimation of the Hemodynamic Response during Motor Imagery Using Bayesian RBF Neural Network

Hemodynamic response during motor imagery(MI)b studied extensively by functional magnetic resonance imaging(fMRI)technologies.To further understand the human brain functions under MI,a more precise classification of the brain regions corresponding to each brain function b desired.In this study,a Bayesian trained radial basis function(RBF)neural network,which determines the weights and regularization parameters automatically by Bayesian learning,is applied to make a precise classification of the hemodynamic response to the tasks during the MI experiment.To illustrate the proposed method,data with MI task performance from 1 subject was used.The results demonstrate that this approach splits the hemodynamic response to different tasks successfully.     

HRF estimation in fMRI data with an unknown drift matrix by iterative minimization of the Kullback-Leibler divergence

Hemodynamic response function (HRF) estimation in noisy functional magnetic resonance imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Nonparametric methods which allow more flexibility in the estimation by inferring the HRF at each time sample have provided improved performance in comparison to the parametric methods. In this paper, the mixed-effects model is used to derive a new algorithm for nonparametric maximum likelihood HRF estimation. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix. This allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component. Estimates of the HRF and the hyperparameters are derived by iterative minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The performance of proposed method is demonstrated on simulated and real fMRI data, the latter originating from both event-related and block design fMRI experiments.     

Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model

Mapping of functional magnetic resonance imaging (fMRI) to conventional anatomical MRI is a valuable step in the interpretation of fMRI activations. One of the main limits on the accuracy of this alignment arises from differences in the geometric distortion induced by magnetic field inhomogeneity. This paper describes an approach to the registration of echo planar image (EPI) data to conventional anatomical images which takes into account this difference in geometric distortion. We make use of an additional spin echo EPI image and use the known signal conservation in spin echo distortion to derive a specialized multimodality nonrigid registration algorithm. We also examine a plausible modification using log-intensity evaluation of the criterion to provide increased sensitivity in areas of low EPI signal. A phantom-based imaging experiment is used to evaluate the behavior of the different criteria, comparing nonrigid displacement estimates to those provided by a imagnetic field mapping acquisition. The algorithm is then applied to a range of nine brain imaging studies illustrating global and local improvement in the anatomical alignment and localization of fMRI activations.     

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.     

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.