Anthony J. Bell

Analysis of fMRI Data by Blind Separation Into Independent Spatial Components

Current analytical techniques applied to functional magnetic resonance imaging (fMRI) data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Here we describe a new method for analyzing fMRI data based on the independent component analysis (ICA) algorithm of Bell and Sejnowski ([1995]: Neural Comput 7:1129–1159). We decomposed eight fMRI data sets from 4 normal subjects performing Stroop color‐naming, the Brown and Peterson word/number task, and control tasks into spatially independent components. Each component consisted of voxel values at fixed three‐dimensional locations (a component “map”), and a unique associated time course of activation. Given data from 144 time points collected during a 6‐min trial, ICA extracted an equal number of spatially independent components. In all eight trials, ICA derived one and only one component with a time course closely matching the time course of 40‐sec alternations between experimental and control tasks. The regions of maximum activity in these consistently task‐related components generally overlapped active regions detected by standard correlational analysis, but included frontal regions not detected by correlation. Time courses of other ICA components were transiently task‐related, quasiperiodic, or slowly varying. By utilizing higher‐order statistics to enforce successively stricter criteria for spatial independence between component maps, both the ICA algorithm and a related fourth‐order decomposition technique (Comon [1994]: Signal Processing 36:11–20) were superior to principal component analysis (PCA) in determining the spatial and temporal extent of task‐related activation. For each subject, the time courses and active regions of the task‐related ICA components were consistent across trials and were robust to the addition of simulated noise. Simulated movement artifact and simulated task‐related activations added to actual fMRI data were clearly separated by the algorithm. ICA can be used to distinguish between nontask‐related signal components, movements, and other artifacts, as well as consistently or transiently task‐related fMRI activations, based on only weak assumptions about their spatial distributions and without a priori assumptions about their time courses. ICA appears to be a highly promising method for the analysis of fMRI data from normal and clinical populations, especially for uncovering unpredictable transient patterns of brain activity associated with performance of psychomotor tasks. Hum. Brain Mapping 6:160–188, 1998.

Imaging brain dynamics using independent component analysis

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.

A Unifying Information-Theoretic Framework for Independent Component Analysis

Abstract We show that different theories recently proposed for independent component analysis (ICA) lead to the same iterative learning algorithm for blind separation of mixed independent sources. We review those theories and suggest that information theory can be used to unify several lines of research. Pearlmutter and Parra [1] and Cardoso [2] showed that the infomax approach of Bell and Sejnowski [3] and the maximum likelihood estimation approach are equivalent. We show that negentropy maximization also has equivalent properties, and therefore, all three approaches yield the same learning rule for a fixed nonlinearity. Girolami and Fyfe [4] have shown that the nonlinear principal component analysis (PCA) algorithm of Karhunen and Joutsensalo [5] and Oja [6] can also be viewed from information-theoretic principles since it minimizes the sum of squares of the fourth-order marginal cumulants, and therefore, approximately minimizes the mutual information [7]. Lambert [8] has proposed different Bussgang cost functions for multichannel blind deconvolution. We show how the Bussgang property relates to the infomax principle. Finally, we discuss convergence and stability as well as future research issues in blind source separation.

Blind Separation of Delayed and Convolved Sources

We address the difficult problem of separating multiple speakers with multiple microphones in a real room. We combine the work of Torkkola and Amari, Cichocki and Yang, to give Natural Gradient information maximisation rules for recurrent (IIR) networks, blindly adjusting delays, separating and deconvolving mixed signals. While they work well on simulated data, these rules fail in real rooms which usually involve non-minimum phase transfer functions, not-invertible using stable IIR filters. An approach that sidesteps this problem is to perform infomax on a feedforward architecture in the frequency domain (Lambert 1996). We demonstrate real-room separation of two natural signals using this approach.

Blind source separation of real world signals

We present a method to separate and deconvolve sources which have been recorded in real environments. The use of noncausal FIR filters allows us to deal with nonminimum mixing systems. The learning rules can be derived from different viewpoints such as information maximization, maximum likelihood and negentropy which result in similar rules for the weight update. We transform the learning rule into the frequency domain where the convolution and deconvolution property becomes a multiplication and division operation. In particular the FIR polynomial algebra techniques as used by Lambert present an efficient tool to solve true phase inverse systems allowing a simple implementation of noncausal filters. The significance of the methods is shown by the successful separation of two voices and separating a voice that has been recorded with loud music in the background. The recognition rate of an automatic speech recognition system is increased after separating the speech signals.

Blind separation of multiple speakers in a multipath environment

We relate information theoretic blind learning methods (infomax) and Bussgang blind equalization methods. The multipath extension of blind source separation methods can be seen in the frequency domain using FIR matrix algebra (matrices of finite impulse response filters). Three forms of Bussgang algorithms are given. The blind serial update method of Cardoso and Laheld (1994) is related to the infomax objective of Bell and Sejnowski (1995). The application emphasis is on speech separation. We demonstrate the robustness and power of the new techniques by blindly separating speech signals recorded in a multipath environment.

Blind separation and blind deconvolution: an information-theoretic approach

Blind separation and blind deconvolution are related problems in unsupervised learning. In this contribution, static non-linearities are used in combination with an information-theoretic objective function, making the approach more rigorous than previous ones. We derive a new algorithm and with it perform nearly perfect separation of up to 10 digitally mixed human speakers, better performance than any previous algorithms for blind separation. When used for deconvolution, the technique automatically cancels echoes and reverberations and reverses the effects of low-pass filtering.

Independent Component Analysis of Electroencephalographic and Event-Related Potential Data

The electroencephalogram (EEG) is a non-invasive measure of brain electrical activity recorded as changes in potential difference between points on the human scalp. Because of volume conduction through cerebrospinal fluid, skull and scalp, EEG data collected from any point on the scalp includes activity from processes occurring within a large brain volume.