INDEPENDENT COMPONENT ANALYSIS AND BEYOND IN BRAIN IMAGING: EEG,MEG, FMRI, AND PET

Jagath C. Rajapakse�, Andrzej Cichocki�, and V. David Sanchez A.�

�School of Computer Engineering, Nanyang Technological University, Singapore�Laboratory of Advanced Brain Signal Processing, Brain Science Institute, RIKEN , Japan

�Advanced Computational Intelligent Systems, Pasadena, CA, USAemail: asjagath@ntu.edu.sg, cia@bsp.brain.riken.go.jp, vdavidsanchez@earthlink.net

Abstract

There is an increasing interest in analyzing brain imagesfrom various imaging modalities, that record the brain ac-tivity during functional task, for understanding how thebrain functions as well as for the diagnosis and treatment ofbrain disease. Independent Component Analysis (ICA), anexploratory and unsupervised technique, separates varioussignal sources mixed in brain imaging signals such as brainactivation and noise, assuming that the sources are mutuallyindependent in the complete statistical sense [1]. This papersummarizes various applications of ICA in processing brainimaging signals: EEG, MEG, fMRI or PET. We highlightthe current issues and limitations of applying ICA in theseapplications, current, and future directions of research.

Key Words: Blind signal and image processing, higherorder statistics, independent component analysis, statisticalindependence.

1. INTRODUCTION

Functional brain imaging modalities, such as electroen-cephalography (EEG), magnetoencephalography (MEG),functional magnetic resonance imaging (fMRI), andpositron emission tomography (PET) provides functionalinformation about the activity of neurons or their populationduring sensory or cognitive tasks. One of the most impor-tant challenges of brain imaging is the localization of spe-cific brain areas that carry out certain functions and mon-itoring the ongoing brain activity over time [2]. In orderto achieve this, it is often necessary to separate the signalsinvolved in brain processes from their artifacts.

In imaging neuroscience, mostly referred as brain imag-ing, as in other signal processing areas, a common task isto find an adequate representation of multivariate data forsubsequent processing and interpretation. The transformedvariables are then envisaged to optimally represent the es-sential structure of data, that can provide information aboutthe process of generation of underlying events. The focus

of this paper is the application of Independent ComponentAnalysis (ICA) to the analysis of brain signals that presumethat the brain processes and the other noise and artifactualcomponents are mutually independent in complete statisti-cal sense.

The basic model assumed in ICA for brain imaging is asfollows:

���� � ����� � ���� (1)

where ���� � ������� ������ � � � ������� � �� indicates azero mean vector of signals observed by the imaging modal-ity at time �, ���� � �� denotes � number of sources, atmost one Gaussian, that generate the observed brain signals,and ���� � �� indicate the noise embedded in the signal.The matrix � is a full column rank ��� matrix, (� � �),that represents a linear mixing of the sources embedded inthe observed brain signals. The mixing is assumed instanta-neous, i.e., that there is no time delay between the sourcesof events in the brain and the observed signals. The chal-lenge of identifying brain signal sources can then be posedas the realization of source signals ����, given the observa-tions ���� and an unknown mixing matrix �. If no furtherassumptions are made, the noise can be included in the sig-nals as a source signal component.

A set of sources is said to be independent in complete sta-tistical sense if their joint density is equal to the product ofthe marginal densities. The concept of statistical indepen-dence may be defined by means of an independence crite-rion derived from the statistical properties of the data, suchas entropy of output sources [3], non-Gaussianity [4], etc.Based on these properties, an objective function or contrastfunction is derived. To optimize this function, the sourcesignals are separated to be as independent as possible. En-tropy is a criterion based on the amount of information con-tained in some occurrences of a discrete random variable[5]. The invariance to invertible linear transforms and non-negativity are introduced by using the concepts of negen-tropy and mutual information (MI) [3]. Minimizing the MIbetween the outputs of a system is equivalent to maximizing

individual negentropies of its outputs, which can be provedby means of expressing the two items via the Kullback-Leibler divergence [6, 7].

The current algorithms for ICA can loosely be classifiedin two categories. One category contains adaptive algo-rithms generally based on stochastic gradient methods andimplemented in neural networks [3, 6]. The neural adaptivealgorithms exhibit slow convergence and their convergencedepends crucially on the correct choice of the learning rateparameters. The second category relies on batch computa-tion optimizing some relevant criterion functions [8]. Thestatistical properties the ICA, such as consistency, asymp-totic variance, robustness depend on the choice of the con-trast function whereas the algorithmic properties, such asconvergence speed, memory requirements, numerical sta-bility, depend on the optimization algorithm.

Source separation consists of funding a demixing matrix�, without resorting to any information about the mixingmatrix �, so that the elements of the estimated source vec-tor become as independent as possible:

����� ������ (2)

After performing ICA, it is expected that the separatingmatrix � converges to a fixed value which should ide-ally be equal to the pseudo-inverse of the mixing matrix:� � ���������. ICA involving higher-order statisticsof sources is one of the approaches for Blind Source Separa-tion (BSS). It sometimes only consider second-order statis-tics. An up-to-date review of the state of the art in BSS/ICAis provided in [9]; frontiers of research in this area are sum-marized in [10].

Applications of ICA show special promises in the areasof non-invasive human brain imaging techniques to delin-eate the neural processes that underlie human cognition andsensori-motor functions. To understand human neurophysi-ology, we rely on several types of non-invasive neuroimag-ing techniques: EEG, MEG, and functional MRI (fMRI).While each of these techniques is useful, there is no singletechnique that provides both the spatial and temporal res-olution necessary to make inferences about the intracranialbrain sources of activity. The application of ICA in brainimaging has two purposes: noise reduction and location de-tection of brain activation. Very recently, several researchgroups have demonstrated that the techniques and methodsof BSS are related to those currently used in electromag-netic source localization (ESL) [1].

2. EEG AND MEG DATA PROCESSING

When a region of neural tissue (consisting of about 100,000or more neurons) is synchronously active, detectable ex-tracellular electric currents and magnetic fields are gener-ated. These regions of activity can be modeled as “cur-

Dipolar brain sources

} MEG or EEGsignals

Fig. 1. Conceptual models for generation of EEG/MEG sig-nals

rent dipoles” because they generate a dipolar electric cur-rent field in the surrounding volume of the head. These ex-tracellular currents flow throughout the volume of the headand create potential differences on the surface of the headthat can be detected with surface electrodes in a procedurecalled electroencephalography (EEG). One can also placesuper-conducting coils above the head and detect the mag-netic fields generated by the activity in a procedure calledmagnetoencephalography (MEG). (see Figure 2).

Neural activity in the cerebral cortex generates smallelectric currents which create potential differences on thesurface of the scalp (detected by EEG) as well as very smallmagnetic fields which can be detected using SQUIDs (Su-perConducting QUantum Interference Devices). The great-est benefit of MEG is that it provides information that iscomplementary to EEG. In addition, the magnetic fields(unlike the electric currents) are not distorted by the inter-vening biological mass. Under certain circumstances, thisallows precise localization of the neural currents responsi-ble for the measured magnetic field.

If one knows the positions and orientations of the sourcesin the brain, one can calculate the patterns of electric po-tentials or magnetic fields on the surface of the head. Thisis called the forward problem. If otherwise, one has onlythe patterns of electric potential or magnetic fields, thenone needs to calculate the locations and orientations of thesources. This is called the inverse problem. Inverse prob-lems are notoriously more difficult to solve than forwardproblems. In this case, given only the electric potentials andmagnetic fields on the surface, there is no unique solution tothe problem. The only hope is that there is some additionalinformation available that can be used to constrain the infi-nite set of possible solutions to a single unique solution.

Determining which regions of the brain are active, givenEEG/MEG measurements on the scalp level is an important

problem. An accurate and reliable solution to such a prob-lem can give information about the higher brain functionsand patient-specific cortical activity. However, estimat-ing the location and distribution of electric current sourceswithin the brain from EEG/MEG recordings is an ill-posedproblem, because there is no unique solution and the so-lution does not depend continuously on the data. The ill-posedness of the problem and the distortion of sensor sig-nals by large noise sources make finding a correct solutiona challenging analytic and computational problem.

In the ICA approach, the sources of activation are consid-ered temporally independent to artifacts and interferences:eye and muscle activity, line noise, and cardiac signals,which are assumed not to be time-locked to the sources ofEEG activity conceived to reflect the synaptic activity ofcortical neurons. Signal propagation is supposed instanta-neously and summation of currents at the scalp sensors isconsidered essentially linear.

ERP time courses recorded from the human scalp aregenerally averaged prior to their analysis to increase theirsignal/noise ratio relative to other non-time and phaselocked EEG activity and non-neural artifacts [11]. Thesource distributions are mostly super-Gaussian since an av-eraged ERP is composed of one or more overlapping se-ries of relatively brief activations within spatially fixed brainareas performing separable stages of stimulus informationprocessing. The super-Gaussian statistics of independentcomponents of ERP data may indicate that brain informa-tion processing is dominated by spatially sparse, intermit-tently synchronous brain structures. The number of sen-sors is supposed to be at least equal to the number of signalsources, though this is highly questionable.

The statistical estimation of the source components fromobserved EEG signals should be performed irrespective ofthe physical locations or configuration of the sources. ICAis therefore useful in solving the elimination of artifactualsignals and the source identification problem in EEG/MEGsignal processing. The EEG/MEG data can be first decom-posed into useful signal and noise subspaces using standardtechniques like local and robust PCA, SVD and nonlinearadaptive filtering. Next, we apply ICA algorithms to decom-pose the observed signals (signal subspace) into indepen-dent components. The ICA approach enables us to projecteach independent component (independent “brain source”)onto an activation map at the skull level.

2.1. Noise and Interference Cancellation

One important problem in brain imaging is how to automat-ically detect, extract and eliminate noise and artifacts. An-other related problem is how to classify independent “brainsources” and artifacts. The automatic on-line eliminationof artifacts and other interference sources is especially im-portant for extended recordings, e.g., EEG/MEG recording

during sleep. For each activation map, we can perform nextan EEG/MEG source localization procedure, looking onlyfor a single dipole (or 2 dipole) per map. By localizing mul-tiple dipoles independently, we can dramatically reduce thecomplexity of the computation and increase the likelihoodof efficiently converging to the correct and reliable solution.

ICA separates the source components based on thehigher-order statistics of their distributions over time, whichfacilitates the differentiation between strictly periodical sig-nals and regularly and irregularly occurring signals. Manyartifactual signals in both EEG/ERP and MEG recordingsare irregular in nature [12]. The assumption that EEG/MEGsignals are different from artifacts and that their correspond-ing time courses are statistically independent enable theirseparation using the ICA. The independence of ERP signalsand artifacts is valid in many cases by the known differ-ences in physiological origins of those signals. Artifact-freeEEG/MEG signals can be restored by back projection ontothe data space of the remained estimated components afterall presumable artifactual activities were discarded (Figure2.1) [13]. The ICA method uses spatial filters after decom-position to filter artifactual signals and back-project only thesignificant source signals for their reconstruction. PCA isunable to completely separate eye artifacts from brain activ-ity, particularly at comparable amplitudes, indicating that,in this application, the correlation is a weaker assumption.

The problem formulation can be stated in the followingform: Denote by ���� the observed �-dimensional vectorof noisy signals that must be “cleaned” from noise and in-terference. Here we have two types of noise. The first oneis the so called “inner” noise generated by some primarysources that cannot be observed directly but is contained inthe observations. They are mixtures of useful signals andrandom noise signals or other undesirable sources. The sec-ond type of noise is the sensor additive noise (observationerrors) at the output of the measurement system. This noiseis not directly measurable, either. We also assume that someuseful sources are not necessarily statistically independent.Therefore, we cannot achieve perfect separation of primarysources by using any ICA procedure. However, our purposehere is not the separation of the sources but the removal ofindependent or uncorrelated noise components.

The scheme of noise and interference cancellation isshown in Figure (2). ������ � � �� �� � � � � denote the sep-arated independent components from data; �� ���� indicatesthe postprocessed components. The projection of interest-ing or useful independent components (e.g., independent ac-tivation maps) ������ back onto the sensors (electrodes) canbe done by the transformation ����� ��������, where��

is the pseudo-inverse of the unmixing matrix�. In the typ-ical case, where the number of independent components isequal to the number of sensors, we have �� � ���. Acommon technique for noise reduction is to split the signal

in two or more bands. The high-pass bands are subject to athreshold nonlinearity that suppresses low amplitude valueswhile retaining high amplitude values [14].

W�

1�W

SensorSignals

DemixingSystem

BSS/ICA

OptionalNonlinearAdaptive

Filters

InverseSystem

ReconstructedSensorsSignals

NAF

NAF

NAF

DecisionBlocks

�

On-lineswitching

0 or 1

1x

ny �

mx

mx

2x

1y

2y 2x

1x1y

2y

ny

1~y

2~y

ny~

Fig. 2. Conceptual models for removing undesirable com-ponents like noise and artifacts and enhancing multi-sensory(e.g., EEG/MEG) data using nonlinear adaptive filters andhard switches .

Principal Component Analysis (PCA) is a standard tech-nique for the computation of eigenvectors and eigenvaluesof an estimated autocorrelation matrix of raw sensor datathat enables not only reduction in the noise level, but alsoallows us to estimate the number of sources [15]. This ap-proach has been applied to noise reduction in electroen-cephalographic signals. A problem arising from this ap-proach, however, is how to correctly set or estimate thethreshold which divides eigenvalues into the two subsets,especially when the noise is large, i.e., the SNR is low [15].

Recently, it has been realized that ICA or at least com-bining both techniques: PCA and ICA, is more appropriatefor noise reduction and moreover such approach reveal theunderlying structure of signals better than PCA alone [14],[16], [12]. Moreover, using ICA we can achieve better re-sults in the sense that PCA use only second-order statistics,but ICA can estimate a better basis by taking into accounthigher-order statistics inherent in the data and allow to buildnonlinear estimator instead of linear one. ICA algorithmscan be also robust, what is very important for noise can-cellation applications. ICA allows to separate sources ����based on observations ���� using a maximum a posteriorimethod that is disposed of a priory information problem andallows to realize blind scenario. Using ICA we can find in-dependent components, which are undesirable and can bethought of as noisy sources and eliminated.

It should be noted that the uncorrelated principal compo-nents are ordered by decreasing value, while independentcomponents (ICs) are typically extracted without any or-der. We can apply first ICA and next ordering the indepen-dent components (ICs) according to the decreasing abso-lute value of their normalized kurtosis rather than their vari-

ances; since the normalized kurtosis ������ �����

��

�������� is

a natural measure for Gaussianity of signals. Using ������,we can easily detect and remove white (colored) Gaussiannoise form raw sensory data. Optionally we can use morerobust measures to detect and classify specific ICs [17].

2.2. Source Localization

−1 0 1 2 3 4 5

MEG sample

−1 0 1 2 3 4 5

8

7

6

5

4

3

2

1

ICA

−1 0 1 2 3 4 5

8

7

6

5

4

3

2

1

PCA

(a) (b) (c) (d)

Fig. 3. (a) A subset of 122-MEG channels in an auditoryexperiment. (b) Independent and (c) Principal componentsof data. In (d) the superposition of the localizations of thedipole originating and IC2 onto MRI of the subject.

Figure 3 illustrates an example of a promising applicationof blind source separation (BSS) and independent compo-nent analysis (ICA) algorithms for localization of the brainsource signals activated after the auditory and somatosen-sory stimulus applied simultaneously. In the MEG experi-ments performed in collaboration with the Helsinki Univer-sity of Technology, Finland, the stimulus presented to thesubject was produced with a sub-woofer, and the acousticenergy was transmitted to the shielded-room via a plastictube with a balloon at the end [15]. The subject had hishands in contact with the balloon and sensed the vibration.In addition, the sound produced by the sub-woofer was lis-tened to by the subject, constituting the auditory stimula-tion. Using ICA, we successfully extracted auditory and so-matosensory evoked fields (AEF and SEF, respectively) andlocalized the corresponding brain sources [15] (see Figure3).

In addition to denoising and artifacts removal, ICA/BSStechniques can be used to decompose EEG/MEG data intoseparate components, each representing a physiologicallydistinct process or brain source. The main idea here is to

apply localization and imaging methods to each of thesecomponents in turn. The decomposition is usually based onthe underlying assumption of statistical independence be-tween the activation of different cell assemblies involved.An alternative criterion for decomposition is temporal pre-dictability or smoothness of components. These approacheslead to interesting new ways of investigating and analyzingbrain data and developing new hypotheses how the neuralassemblies communicate and process information. This isactually a very extensive and potentially promising researcharea, however these approaches still remain to be validatedat least experimentally.

Recent results have shown by means of ICA that somefeatures of an evoked response may actually be producedby event-related changes in the autocorrelation and cross-correlation structure of the ongoing EEG processes [18].This reflects that synchronous activity in the brain occurscontinuously in some brain regions or by small perturba-tions in their dynamics. It comes out that applying ICA toEEG/ERP data may constitute a potential source of infor-mation on mechanisms of neural synchronization.

3. FUNCTIONAL MRI AND PET

Although EEG/MEG signals are good for monitoring theelectrical and magnetic field activity over the skull, spatialresolution depicted by EEG/MEG signals over the brain islimited. Based on the change of local blood supply for ac-tive neurons, PET and fMRI provide brain imaging signalsfrom the whole brain at a much higher resolution. By meansof short-lived isotopes that emit positrons, PET allows mea-suring the rate of blood flow through particular regions ofthe brain. The basic framework for the analysis of imagingtime series was developed in PET neuroimaging and there-after extended up to fMRI. The basic assumption is that anincrease in neuronal activity within a brain region entailsan increase in local blood flow, leading to reduced con-centrations of deoxyhemoglobin, which has a differentialmagnetic susceptibility in relation to the surrounding tissue.Therefore, relative decreases in deoxyhemoglobin concen-tration attract a reduction in local field inhomogeneity anda slower decay of the MR signal, resulting in higher inten-sities in T2 weighted images.

FMRI data carry spatio-temporal information of re-sponses of the brain responses activated by some functionaltasks. FMRI data are always confounded by physiologi-cal signals such as cardiac, respiratory, and blood flow, theelectronic noise of the scanners and other environmental ar-tifacts [19, 20, 21, 22]. The detection of the brain activationis usually performed by statistically comparing time-seriescorresponding to each brain voxel with the input stimuliand generating statistical maps. The simplest of these ap-proaches is the correlation analysis [23]. In order to correct

for multiple comparisons and spatial correlations, the sta-tistical maps are further analyzed using the Gaussian Ran-dom Field (GRF) theory, whose approach is referred to asthe statistical parametric mapping (SPM) [24]. Prior to thesimple correlation analysis or the SPM analysis, fMRI datais required to be preprocessed using appropriate denoisingor smoothing filters and correct for artifacts. These prepro-cessing techniques are still mostly ad hoc and tend to alterthe original data.

Recently, ICA has become an increasingly promisingdata-driven approach for the analysis of fMRI data becauseof its capability of separating the components of interest,that are due to task-related brain activation, from othercomponents that are due to interferences and artifacts [20].Therefore, it is unnecessary to preprocess fMRI data beforeusing the ICA technique for the detection of brain activa-tion. Figure (4) shows separation of independent compo-nents on data obtained on a simple visual task: an alternat-ing checker board pattern with a central fixation point wasprojected on an LCD system; subjects were asked to fixateon the point of stimulation. Further experimental details areavailable in [21].

(a) (b) (c)

(d) (e) (f)

Fig. 4. Various activation maps and corresponding time-series separated by spatial ICA in a visual experiment. (a)33th component indicating activation in the visual cortex,(b) 7th component indicating head motion artifacts, (c) 9thcomponent indicating flow artifacts, and (d) 25th compo-nent indicating significant noise. (e) and (f) indicate com-ponents of motor activation.

3.1. Temporal, Spatial and Spatio-Temporal ICA

FMRI data is essentially spatio-temporal as a series of brainscans are acquired over time during a functional experi-ment. Recently, there has been a growing interest in ap-plying ICA to analyze fMRI data in two different ways:spatial ICA (SICA) and temporal ICA (TICA) [20, 25, 26].The premise of ICA application in fMRI analysis is that thetask-unrelated components in fMRI data are either indepen-dent in spatial-domain (SICA) or independent in the time-domain (TICA) to the task-related components. The data isdecomposed into a set of spatially independent componentsin SICA whereas the TICA decomposes fMRI data into aset of temporally independent components.

If the time series corresponding to the th brain voxelis �� � ����� ���� � � � ����

�, the fMRI data set is given bythe matrix, � � �� �� � � � �� � where is the to-tal number of brain voxels and � is the total number ofscans collected over time. SICA is based on the fact thatinput data is decomposed into � spatially independent com-ponents, �� � � � �� �� � � � � such that

� � ��� (3)

where � is the mixing matrix and � � �� �� � � � �� �is the matrix of the independent component maps. � � ����� � ��� � � � � ����

� denotes the � th spatial component map.The decomposition made by TICA can be given by

�� � ��� � ����� (4)

Thus, by taking the transpose, we change the roles of themixing matrix and the independent components. In fact, weconsider both matrices as being independent variable enti-ties as much as possible. This is the basic idea in spatio-temporal ICA [15].

In SICA, the multifocal brain areas activated due to asensory or cognitive task are presumed to be unrelated tothe brain regions that are affected by the artifacts and con-founds. The signals due to heartbeat, respiration, and bloodflow can be considered as mutually independent in time-domain because they have frequencies that are differentfrom the task. On the other hand, the spatial independenceof the effect of these signals in the brain is questionable be-cause the influence of noise and interference is common tomost regions of the brain. Furthermore, the motion arti-facts which may be transiently task-related, appear in themost part of the brain indiscriminately. Therefore, some ofthe sources in fMRI data are deterministic in nature and theassociated component maps may not be unrelated spatiallybut may be independent in time because their characteristicsdiffer in time-domain. Therefore, it is more appropriate toassume that these noise and interference sources involvedin fMRI data are independent in time-domain rather thanin the spatial-domain. However, to date, SICA has domi-nated most applications, mainly, because the computational

requirements of TICA has been much higher than those ofthe SICA. The SICA approach is biased towards finding rel-atively sparse and discrete components, and the task-relatedcomponent might split into several ICA components associ-ated to smaller active areas with closely related time-courses[20]; if a number of independent brain processes are activeduring the task, the task-related activation may appear indifferent component maps. Furthermore, if two componentprocesses contributed by the input stimulation appear in awell-overlapped brain area, the ICA may split the resultingactivation areas into many component maps.

In general, TICA is preferable to SICA because mostnon-task related signals are more likely to be independentin time-domain. However, because the number of voxelsof fMRI data in the spatial domain is large, applications ofTICA is prohibitive in practice. In simple experiments likethe finger tapping paradigm, it has been demonstrated thatSICA and TICA produce similar results [27]. However, arecent study [26] using especially designed visual activationparadigms each consisting of two spatio-temporal compo-nents that were either spatially or temporally uncorrelatedhas shown that the independent components produced bydifferent ICA approaches may be task-dependent. There-fore, the independent components of fMRI data, producedby SICA and TICA, may be valid depending on the task.A combination of SICA and TICA has also been consid-ered by Stone et. al. [28], but its limitations are obvious asit is more difficult to design both spatially and temporallyindependent task approaches that are independent to otherinterference and noise as well.

3.2. Detection and Significance of Activation Maps

ICA-based decomposition of fMRI signals is consistentwith fundamental neurophysiological principles concerningthe spatial extent of neural activity during the performanceof psychomotor tasks. Artifacts that make up the bulk of thevariability in the measured fMRI data should have spatialpatterns of activity separate from the localization of brainareas involved in task-related activation. After separation ofindependent components, it remains to select the map cor-responding to actual brain activation. This is currently donepost hoc, correlating the time-series corresponding to com-ponent maps with those of the input stimuli and finding thecomponent giving rise to the maximum correlation [20]. Anattempt to incorporate the input stimuli as reference signal isalso reported in [29]. This approach has the computationaladvantages by producing only the task-related componentin ICA.

When a correlation approach is used in fMRI, it is cus-tomary to express the activation with a certain level of sig-nificance. The ICA model does not provide a significanceestimate for the activation of each separated component,what obscures the result interpretation. In fMRI applica-

tions, by placing ICA in a regression framework, it may bepossible to combine some of the ICA benefits with the ben-efits of the hypothesis-testing approach.

4. CURRENT AND FUTURE DIRECTIONS

There is a current trend in linear ICA/BSS to investigatethe average eigen-structure of a large set of data matriceswhich are functions of available data (typically, covarianceor cumulant matrices for different time delays). In otherwords, the objective is to extract reliable information (likefor example, estimation of sources and/or the mixing ma-trix) from the eigen-structure of a possibly large set of datamatrices. However, since in practice only a finite numberof samples of signals corrupted by noise is available, thedata matrices do not exactly share the same eigen-structure.Furthermore, it should be noted that determining the eigen-structure on the basis of one or even two data matrices leadsusually to poor or unsatisfactory results because such matri-ces, based usually on arbitrary choice, may have some de-generate eigenvalues and they usually discard informationcontained in other data matrices. Therefore, from a statisti-cal point of view, in order to provide robustness and accu-racy, it is necessary to consider the average eigen-structureby taking into account simultaneously a possibly large set ofdata matrices. Several very promising algorithms like Ro-bust SOBI, JADE with time delayed cumulants, and SEONSexploit average eigen-structure and enable us to estimate re-liable sources and the mixing matrix for noisy data [1].

Very recently, research and development has moved thefield toward more general non-independent and/or nonlin-ear source separation approaches. The main objective is todevelop and investigate novel criteria which enable to sep-arate sources which are not precisely independent by usingvarious criteria like linear predictability, smoothness, Kol-mogorov complexity, and sparsity. Also semi blind con-cepts are further investigated where some a priori knowl-edge is exploited, e.g., knowledge about the source distri-bution.

There are still many open and challenging problems likethe following:

1. What are meaningful cost functions which enable us toestimate brain sources which are not completely inde-pendent.

2. Are brain signals nonlinearly mixed?

3. If yes, which nonlinear model is valid.

4. How to estimate the number of sources and their wave-forms if recorded biological data is corrupted by a largeamount of noise, and external and internal interference(e.g., on- going brain activities).

5. How to facilitate the linear or nonlinear BSS problemby incorporating prior knowledge?

The independence assumption may not provide a uniquedecomposition of the data and may not be the desired repre-sentation of the brain imaging data. Nevertheless, ICA maybe useful in noise cancellation or in discerning activation inan exploratory manner. For example, to determine differen-tially activated brain regions such as those transiently taskrelated due to arousal and alertness, or independent brainprocessors involved during a particular task.

The ICA approach is meaningful only if the amount ofdata processed by the algorithm is large enough and the in-dependence assumption holds. Even so, the results are in-fluenced by the assumption that the sources of artifacts andcerebral activity remain spatially stationary through time,which is not always true all over the trials. There shouldbe some means to validate ICA decompositions. One wayis to simulate the conditions under which IC is likely to faillike simulated EEG recordings generated from a head modeland dipole sources that include intrinsic noise and sensornoise, when the number of sources is larger then the numberof sensors. Another approach is based on simultaneouslyrecording and analyzing the correlation of concurrent typesof signal, such as EEG and fMRI, which have good tempo-ral (EEG) and good spatial (fMRI) resolution, respectively.

5. CONCLUSIONS

ICA identifies sources with independent and sparse dynam-ics that may or may not be neuro-anatomically/functionallysegregated. ICA effectively removes artifacts and separatethe sources of the brain signals on the basis of minimal sup-positions on their underlying distributions and further de-composes the remained mixed signals into subcomponentsthat may reflect the activity of functionally distinct genera-tors of physiological activity. The limits of the usefulnessof ICA for EEG, MEG, fMRI and PET analysis will ul-timately depend on the matching between the underlyingassumptions of the analysis and the composition of the ex-perimental data. ICA appears to be well-suited for noisereduction; whether it is a good approach to detect brain ac-tivation remains to be further investigated and validated.

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