The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signals from these recordings. A similar approach is proving useful for analyzing functional magnetic resonance brain imaging (fMRI) data. In this paper, we outline the assumptions underlying ICA and demonstrate its application to a variety of electrical and hemodynamic recordings from the human brain. Keywords—Blind source separation, EEG, fMRI, independent component analysis.

Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'model-free' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ability to quantify statistical significance. We present an integrated approach to Probabilistic ICA for FMRI data that allows for non-square mixing in the presence of Gaussian noise. We employ an objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e. the number of activation and non-Gaussian noise sources. Reduction of the data to this 'true' subspace before the ICA decomposition automatically results in an estimate of the noise, leading to the ability to assign significance to voxels in ICA spatial maps. Estimation of the number of intrinsic sources not only enables us to carry out probabilistic modelling, but also achieves an asymptotically unique decomposition of the data. This reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal pre-whitening and variance normafisation of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternative-hypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and complex artificial FMRI data, and compared to the spatio-temporal accuracy of restfits obtaine...

Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. When the information about the mixing process and sources is limited, the problem is called ‘blind’. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that solutions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous non-sparse methods. Indeed, sparse methods provide a powerful approach to the separation of linear mixtures of independent data. This paper surveys the recent arrival of sparse blind source separation methods and the previously existing non-sparse methods, providing insights and appropriate hooks into the literature along the way.

We apply nine analytic methods employed currently in imaging neuroscience to simulated and actual BOLD fMRI signals and compare their performances under each signal type. Starting with baseline time series generated by a resting subject during a null hypothesis study, we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple, convolved with spatially varying hemodynamic responses, and highly spatially interactive. We then apply these same nine methods to BOLD fMRI time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study. Paired comparisons of results across methods include a voxel-specific concordance correlation

Biomedical signals from many sources including hearts, brains and endocrine systems pose a challenge to researchers who may have to separate weak signals arriving from multiple sources contaminated with artifacts and noise. The analysis of these signals is important both for research and for medical diagnosis and treatment. The applications of Independent Component Analysis (ICA) to biomedical signals is a rapidly expanding area of research and many groups are now actively engaged in exploring the potential of blind signal separation and signal deconvolution for revealing new information about the brain and body. In this review, we survey some recent applications of ICA to a variety of electrical, magnetic and hemodynamic measurements, drawing primarily from our own research. 1.

fMRI data are commonly analyzed by testing the time course from each voxel against specific hypothesized waveforms, despite the fact that many components of fMRI signals are difficult to specify explicitly. In contrast, purely data-driven techniques, by focusing on the intrinsic structure of the data, lack a direct means to test hypotheses of interest to the examiner. Between these two extremes, there is a role for hybrid methods that use powerful data-driven techniques to fully characterize the data, but also use some a priori hypotheses to guide the analysis. Here we describe such a hybrid technique, HYBICA, which uses the initial characterization of the fMRI data from Independent Component Analysis and allows the experimenter to sequentially combine assumed task-related components so that one can gracefully navigate from a fully data-derived approach to a fully hypothesis-driven approach. We describe the results of testing the method with two artificial and two real data sets. A metric based on the diagnostic Predicted Sum of Squares statistic was used to select the best number of spatially independent components to combine and utilize in a standard regressional framework. The proposed metric provided an objective method to determine whether a more data-driven or a more hypothesis-driven approach was appropriate, depending on the degree of mismatch between the hypothesized reference function and the features in the data. HYBICA provides a robust way to combine the data-derived independent components into a data-derived activation waveform and suitable confounds so that standard statistical analysis can be performed. � 2000 Academic Press Key Words: linear regression; independent component analysis; data decomposition; functional magnetic resonance imaging

Exploratory data-driven methods such as Fuzzy clustering analysis (FCA) and Principal component analysis (PCA) may be considered as hypothesis-generating procedures that are complementary to the hypothesis-led statistical inferential methods in functional magnetic resonance imaging (fMRI). Here, a comparison between FCA and PCA is presented in a systematic fMRI study, with MR data acquired under the null condition, i.e., no activation, with different noise contributions and simulated, varying "activation." The contrast-to-noise (CNR) ratio ranged between 1--10. We found that if fMRI data are corrupted by scanner noise only, FCA and PCA show comparable performance. In the presence of other sources of signal variation (e.g., physiological noise), FCA outperforms PCA in the entire CNR range of interest in fMRI, particularly for low CNR values. The comparison method that we introduced may be used to assess other exploratory approaches such as independent component analysis or neural network-based techniques. Crown Copyright # 2000. Published by Elsevier Science Inc.

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INTRODUCTION In functional magnetic resonance (MR) studies, the groups (clusters) of "activated" voxels are identified either by hypothesis-led methods for which the measured time courses (TCs) are correlated with a predefined model function 1,2 or by exploratory, data-driven approaches such as fuzzy or hard clustering (FCA, HCA), 3--7 principal component analysis (PCA), 8 independent component analysis (ICA), or Kohonen maps (KM), 10 which search for selfsimilar groups of TCs in fMRI data. Once a group of activated voxels is selected, the question arises (this has also been raised by Goutte and McKeown), how well the TCs correlate with each other, i.e., how good is the intragroup homogeneity of the group of TCs. Furthermore, if the group of activated TCs is identified by model-led methods, it may happen that time courses highly correlated with the model function do not necessarily correlate well with each other (in the extreme case, they may not correlate at all).

SOBI is a blind source separation algorithm based on time decorrelation. It uses multiple time autocovariance matrices, and performs joint diagonalization thus being more robust than previous time decorrelation algorithms such as AMUSE. We propose an extension called mdSOBI by using multidimensional autocovariances, which can be calculated for data sets with multidimensional parameterizations such as images or fMRI scans. mdSOBI has the advantage of using the spatial data in all directions, whereas SOBI only uses a single direction. These findings are confirmed by simulations and an application to fMRI analysis, where mdSOBI outperforms SOBI considerably.