{"title": "Independent Component Analysis for Identification of Artifacts in Magnetoencephalographic Recordings", "book": "Advances in Neural Information Processing Systems", "page_first": 229, "page_last": 235, "abstract": "", "full_text": "Independent Component Analysis for \n\nidentification of artifacts in \n\nMagnetoencephalographic recordings \n\nRicardo Vigario1; Veikko J ousmiiki2 , \n\nMatti Hiimiiliiinen2, Riitta Hari2, and Erkki Oja1 \n\n1 Lab. of Computer & Info. Science \nHelsinki University of Technology \n\nP.O. Box 2200, FIN-02015 HUT, Finland \n\n{Ricardo.Vigario, Erkki.Oja}@hut.fi \n\n2 Brain Research Unit, Low Temperature Lab. \n\nHelsinki University of Technology \n\nP.O. Box 2200, FIN-02015 HUT, Finland \n\n{veikko, msh, hari}@neuro.hut.fi \n\nAbstract \n\nWe have studied the application of an independent component analysis \n(ICA) approach to the identification and possible removal of artifacts \nfrom a magnetoencephalographic (MEG) recording. This statistical tech(cid:173)\nnique separates components according to the kurtosis of their amplitude \ndistributions over time, thus distinguishing between strictly periodical \nsignals, and regularly and irregularly occurring signals. Many artifacts \nbelong to the last category. In order to assess the effectiveness of the \nmethod, controlled artifacts were produced, which included saccadic eye \nmovements and blinks, increased muscular tension due to biting and the \npresence of a digital watch inside the magnetically shielded room. The \nresults demonstrate the capability of the method to identify and clearly \nisolate the produced artifacts. \n\n1 Introduction \n\nWhen using a magnetoencephalographic (MEG) record, as a research or clinical tool, the \ninvestigator may face a problem of extracting the essential features of the neuromagnetic \n\n\u2022 Corresponding author \n\n\f230 \n\nR. Vigario, v. Jousmiiki, M. Hiimiiliiinen, R. Hari and E. Oja \n\nsignals in the presence of artifacts. The amplitude of the disturbance may be higher than \nthat of the brain signals, and the artifacts may resemble pathological signals in shape. For \nexample, the heart's electrical activity, captured by the lowest sensors of a whole-scalp \nmagnetometer array, may resemble epileptic spikes and slow waves (Jousmili and Hari \n1996). \n\nThe identification and eventual removal of artifacts is a common problem in electroen(cid:173)\ncephalography (EEG), but has been very infrequently discussed in context to MEG (Hari \n1993; Berg and Scherg 1994). \n\nThe simplest and eventually most commonly used artifact correction method is rejection, \nbased on discarding portions of MEG that coincide with those artifacts. Other methods \ntend to restrict the subject from producing the artifacts (e.g. by asking the subject to fix the \neyes on a target to avoid eye-related artifacts, or to relax to avoid muscular artifacts). The \neffectiveness of those methods can be questionable in studies of neurological patients, or \nother non-co-operative subjects. In eye artifact canceling, other methods are available and \nhave recently been reviewed by Vigario (I 997b) whose method is close to the one presented \nhere, and in Jung et aI. (1998). \nThis paper introduces a new method to separate brain activity from artifacts, based on the \nassumption that the brain activity and the artifacts are anatomically and physiologically \nseparate processes, and that their independence is reflected in the statistical relation be(cid:173)\ntween the magnetic signals generated by those processes. \n\nThe remaining of the paper will include an introduction to the independent component \nanalysis, with a presentation of the algorithm employed and some justification of this ap(cid:173)\nproach. Experimental data are used to illustrate the feasibility of the technique, followed \nby a discussion on the results. \n\n2 Independent Component Analysis \n\nIndependent component analysis is a useful extension of the principal component analysis \n(PC A). It has been developed some years ago in context with blind source separation ap(cid:173)\nplications (Jutten and Herault 1991; Comon 1994). In PCA. the eigenvectors of the signal \ncovariance matrix C = E{xxT } give the directions oflargest variance on the input data \nx. The principal components found by projecting x onto those perpendicular basis vectors \nare uncorrelated, and their directions orthogonal. \n\nHowever, standard PCA is not suited for dealing with non-Gaussian data. Several au(cid:173)\nthors, from the signal processing to the artificial neural network communities, have shown \nthat information obtained from a second-order method such as PCA is not enough and \nhigher-order statistics are needed when dealing with the more demanding restriction of \nindependence (Jutten and Herault 1991; Comon 1994). A good tutorial on neural ICA im(cid:173)\nplementations is available by Karhunen et al. (1997). The particular algorithm used in this \nstudy was presented and derived by Hyvarinen and Oja (1997a. 1997b). \n\n2.1 The model \n\nIn blind source separation, the original independent sources are assumed to be unknown, \nand we only have access to their weighted sum. In this model, the signals recorded in an \nMEG study are noted as xk(i) (i ranging from 1 to L, the number of sensors used, and \nk denoting discrete time); see Fig. 1. Each xk(i) is expressed as the weighted sum of M \n\n\fICAfor Identification of Artifacts in MEG Recordings \n\nindependent signals Sk(j), following the vector expression: \n\nM \n\nXk = La(j)sdj) = ASk, \n\nj=l \n\n231 \n\n(1) \n\nwhere Xk = [xk(1), ... , xk(L)]T is an L-dimensional data vector, made up of the L mix(cid:173)\ntures at discrete time k. The sk(1), ... , sk(M) are the M zero mean independent source \nsignals, and A = [a(1), . .. , a(M)] is a mixing matrix independent of time whose elements \nail are th.e unknown coefficients of the mixtures. In order to perform ICA, it is necessary \nto have at least as many mixtures as there are independent sources (L ~ M). When this \nrelation is not fully guaranteed, and the dimensionality of the problem is high enough, \nwe should expect the first independent components to present clearly the most strongly \nindependent signals, while the last components still consist of mixtures of the remaining \nsignals. In our study, we did expect that the artifacts, being clearly independent from the \nbrain activity, should come out in the first independent components. The remaining of the \nbrain activity (e.g. a and J-L rhythms) may need some further processing. \nThe mixing matrix A is a function of the geometry of the sources and the electrical conduc(cid:173)\ntivities of the brain, cerebrospinal fluid, skull and scalp. Although this matrix is unknown. \nwe assume it to be constant, or slowly changing (to preserve some local constancy). \nThe problem is now to estimate the independent signals Sk (j) from their mixtures, or the \nequivalent problem of finding the separating matrix B that satisfies (see Eq. 1) \n\nIn our algorithm, the solution uses the statistical definition of fourth-order cumulant or \nkurtosis that, for the ith source signal, is defined as \n\nkurt(s(i)) = E{s(i)4} - 3[E{s(i)2}]2, \n\nwhere E( s) denotes the mathematical expectation of s. \n\n(2) \n\n2.2 The algorithm \n\nThe initial step in source separation, using the method described in this article, is whiten(cid:173)\ning, or sphering. This projection of the data is used to achieve the uncorrelation between \nthe solutions found, which is a prerequisite of statistical independence (Hyvarinen and Oja \n1997a). The whitening can as well be seen to ease the separation of the independent sig(cid:173)\nnals (Karhunen et al. 1997). It may be accomplished by PCA projection: v = V x, with \nE{ vvT} = I. The whitening matrix V is given by \nV - A- 1/ 2-=T \n..... , \n\n-\n\nwhere A = diag[-\\(1), ... , -\\(M)] is a diagonal matrix with the eigenvalues of the data \ncovariance matrix E{xxT}, and 8 a matrix with the corresponding eigenvectors as its \ncolumns. \nConsider a linear combination y = w T v of a sphered data vector v, with Ilwll = 1. Then \nE{y2} = .1 andkurt(y) = E{y4}-3, whose gradientwithrespecttow is 4E{v(wTv)3} . \n\nBased on this, Hyvarinen and Oja (1997a) introduced a simple and efficient fixed-point \nalgorithm for computing ICA, calculated over sphered zero-mean vectors v, that is able to \nfind one of the rows of the separating matrix B (noted w) and so identify one independent \nsource at a time -\nthe corresponding independent source can then be found using Eq. 2. \nThis algorithm, a gradient descent over the kurtosis, is defined for a particular k as \n\n1. Take a random initial vector Wo of unit norm. Let l = 1. \n\n\f232 \n\nR. Vigario, v. Jousmiiki, M. Hiimiiliiinen, R. Hari and E. Oja \n\nlarge sample OfVk vectors (say, 1,000 vectors). \n\n2. Let Wi = E{V(W[.1 v)3} - 3Wl-I. The expectation can be estimated using a \n3. Divide Wi by its norm (e.g. the Euclidean norm Ilwll = JLi wI J. \n4. lflwT wi-II is not close enough to 1, let I = 1+1 andgo back to step 2. Otherwise, \n\noutput the vector Wi. \n\nIn order to estimate more than one solution, and up to a maximum of lvI, the algorithm \nmay be run as many times as required. It is, nevertheless, necessary to remove the infonna(cid:173)\ntion contained in the solutions already found, to estimate each time a different independent \ncomponent. This can be achieved, after the fourth step of the algorithm, by simply sub(cid:173)\ntracting the estimated solution s = w T v from the unsphered data Xk . As the solution is \ndefined up to a multiplying constant, the subtracted vector must be multiplied by a vector \ncontaining the regression coefficients over each vector component of Xk. \n\n3 Methods \n\nThe MEG signals were recorded in a magnetically shielded room with a 122-channel \nwhole-scalp Neuromag-122 neuromagnetometer. This device collects data at 61 locations \nover the scalp, using orthogonal double-loop pick-up coils that couple strongly to a local \nsource just underneath, thus making the measurement \"near-sighted\" (HamaHi.inen et al. \n1993). \n\nOne of the authors served as the subject and was seated under the magnetometer. He kept \nhis head immobile during the measurement. He was asked to blink and make horizontal \nsaccades, in order to produce typical ocular artifacts. Moreover, to produce myographic \nartifacts, the subject was asked to bite his teeth for as long as 20 seconds. Yet another \nartifact was created by placing a digital watch one meter away from the helmet into the \nshieded room. Finally, to produce breathing artifacts, a piece of metal was placed next \nto the navel. Vertical and horizontal electro-oculograms (VEOG and HEOG) and electro(cid:173)\ncardiogram (ECG) between both wrists were recorded simultaneously with the MEG, in \norder to guide and ease the identification of the independent components. The bandpass(cid:173)\nfiltered MEG (0.03-90 Hz), VEOG, HEOG, and ECG (0.1-100 Hz) signals were digitized \nat 297 Hz, and further digitally low-pass filtered, with a cutoff frequency of 45 Hz and \ndownsampled by a factor of 2. The total length of the recording was 2 minutes. A second \nset of recordings was perfonned, to assess the reproducibility of the results. \n\nFigure 1 presents a subset of 12 spontaneous MEG signals from the frontal, temporal and \noccipital areas. Due to the dimension of the data (122 magnetic signals were recorded), it \nis impractical to plot all MEG signals (the complete set is available on the internet -\nsee \nreference list for the adress (Vigario 1997a\u00bb. Also both EOG channels and the electrocar(cid:173)\ndiogram are presented. \n\n4 Results \n\nFigure 2 shows sections of9 independent components (IC's) found from the recorded data, \ncorresponding to a I min period, starting 1 min after the beginning of the measurements. \nThe first two IC's, with a broad band spectrum, are clearly due to the musclular activity \noriginated from the biting. Their separation into two components seems to correspond, on \nthe basis of the field patterns, to two different sets of muscles that were activated during \nthe process. IC3 and IC5 are, respectively showing the horizontal eye movements and the \neye blinks, respectively. IC4 represents cardiac artifact that is very clearly extracted. In \nagreement with Jousmaki and Hari (1996), the magnetic field pattern of IC4 shows some \npredominance on the left. \n\n\fICA/or Identification 0/ Artifacts in MEG Recordings \n\n233 \n\nMEG [ 1000 fTlcm \nEOG [ 500 IlV \n\nECG [ 500 IlV \n\nI-- saccades ---l I--\n\nblinking \n\n---l \n\nI-- biting ---l MEG \n\n~\u00b7'104~ M \n\n~=::::::::::::::=:: :: \nrJ. ......... ,J.\\ ....... 1iIIiM~ .. t... 2 t \n:;::::::;:::~= :; \n~::::::::;::= :; \n\n~ \u2022\u2022 \",~Jrt ..,. t \n\n.... ~,.~ . \u2022 .J.. . \n\n.../\\\"\"$\"\"~I 4 ~ \n\n.,............. ................. \" .... Dei ..... \" \n\nI; rp .. I p\", .... , . . . . . . . . . . . . at ... '.... 5 ~ \n\n5 t \n\n., ... ...., ,'fIJ'\\, \n\n,..,d I \u2022 \n\n........ ..-. ,LIlt ... ., \n\n....,..,.\"........ . \n\n.'''IIb'''*. rt \n\n,P .... \n\n, ., ............... ' tMn':M.U \n\n6 t \nU\\..,.--II..------'-__ ooII..Jl,,- VEOG \n\n, ..... ' \n\n... , \n\n-1I\\JY. \u00b7 ---\n\nIt ... 11.1. HEOG \n~UijuJJJ.LU Wl Uij.lJU.LllU.UUUllUUij,UU~ijJJJ ECG \n\n\".'tIItS \n\n10 s \n\nFigure 1: Samples of MEG signals, showing artifacts produced by blinking, saccades, \nbiting and cardiac cycle. For each of the 6 positions shown, the two orthogonal directions \nof the sensors are plotted. \n\nThe breathing artifact was visible in several independent components, e.g. IC6 and IC7. It \nis possible that, in each breathing the relative position and orientation of the metallic piece \nwith respect to the magnetometer has changed. Therefore, the breathing artifact would be \nassociated with more than one column of the mixing matrix A, or to a time varying mixing \nvector. \n\nTo make the analysis less sensible to the breathing artifact, and to find the remaining arti(cid:173)\nfacts, the data were high-pass filtered, with cutoff frequency at 1 Hz. Next, the independent \ncomponent IC8 was found. It shows clearly the artifact originated at the digital watch, \nlocated to the right side of the magnetometer. \n\nThe last independent component shown, relating to the first minute of the measurement, \nshows an independent component that is related to a sensor presenting higher RMS (root \nmean squared) noise than the others. \n\n5 Discussion \n\nThe present paper introduces a new approach to artifact identification from MEG record(cid:173)\nings, based on the statistical technique of Independent Component Analysis. Using this \nmethod, we were able to isolate both eye movement and eye blinking artifacts, as well as \n\n\f234 \n\nR. Vigario, v. Jousmiiki, M HtJmlJliiinen, R. Hari and E. Oja \n\ncardiac, myographic, and respiratory artifacts. \n\nThe basic asswnption made upon the data used in the study is that of independence be(cid:173)\ntween brain and artifact waveforms. In most cases this independence can be verified by the \nknown differences in physiological origins of those signals. Nevertheless, in some event(cid:173)\nrelated potential (ERP) studies (e.g. when using infrequent or painful stimuli), both the \ncerebral and ocular signals can be similarly time-locked to the stimulus. This local time \ndependence could in principle affect these particular ICA studies. However, as the inde(cid:173)\npendence between two signals is a measure of the similarity between their joint amplitude \ndistribution and the product of each signal's distribution (calculated throughout the entire \nsignal, and not only close to the stimulus applied), it can be expected that the very local \nrelation between those two signals, during stimulation, will not affect their global statistical \nrelation. \n\n6 Acknowledgment \n\nSupported by a grant from Junta Nacional de Investiga~ao Cientifica e Tecnologica, under \nits 'Programa PRAXIS XXI' (R.Y.) and the Academy of Finland (R.H.). \n\nReferences \n\nBerg, P. and M. Scherg (1994). A multiple source approach to the correction of eye \n\nartifacts. Electroenceph. clin. Neurophysiol. 90, 229-241. \n\nComon, P. (1994). Independent component analysis - a new concept? Signal Process(cid:173)\n\ning 36,287-314. \n\nHamalainen, M., R. Hari, R. Ilmoniemi, 1. Knuutila, and O. Y. Lounasmaa (1993, April). \nMagnetoencephalography-theory, instrumentation, and applications to noninvasive \nstudies of the working human brain. Reviews o/Modern Physics 65(2), 413-497. \n\nHari, R. (1993). Magnetoencephalography as a tool of clinical neurophysiology. In \nE. Niedermeyer and F. L. da Silva (Eds.), Electroencephalography. Basic princi(cid:173)\nples, clinical applications, and relatedjields, pp. 1035-1061 . Baltimore: Williams \n& Wilkins. \n\nHyvarinen, A. and E. Oja (l997a). A fast fixed-point algorithm for independent compo(cid:173)\n\nnent analysis. Neural Computation (9), 1483-1492. \n\nHyvarinen, A. and E. Oja (1997b). One-unit learning rules for independent component \nanalysis. In Neural Information Processing Systems 9 (Proc. NIPS '96). MIT Press. \nJousmiiki, Y. and R. Hari (1996). Cardiac artifacts in magnetoencephalogram. Journal \n\no/Clinical Neurophysiology 13(2), 172-176. \n\nJung, T.-P., C. Hwnphries, T.-W. Lee, S. Makeig, M. J. McKeown, Y. lragui, and \nT. Sejnowski (1998). Extended ica removes artifacts from electroencephalographic \nrecordings. In Neural Information Processing Systems 10 (Proc. NIPS '97). MIT \nPress. \n\nJutten, C. and 1. Herault (1991). Blind separation of sources, part i: an adaptive algo(cid:173)\n\nrithm based on neuromimetic architecture. Signal Processing 24, 1-10. \n\nKarhunen, J., E. Oja, L. Wang, R. Vigmo, and J. Joutsensalo (1997). A class of neural \nnetworks for independent component analysis. IEEE Trans. Neural Networks 8(3), \n1-19. \n\nVigmo, R. (1997a). WWW adress for the MEG data: \nhttp://nuc1eus.hut.firrvigarioINIPS97 _data.html. \n\nVigmo, R. (1997b). Extraction of ocular artifacts from eeg using independent compo(cid:173)\n\nnent analysis. To appear in Electroenceph. c/in. Neurophysiol. \n\n\fICAfor Identification of Artifacts in MEG Recordings \n\n235 \n\nIC1 ~~~ \n------,--y~-------------------------.-.------~~ .. , .. U ~ . . . \n\nIC2 \n\n~''' ... '' .. ' \n\\ \n<> . \n.\\ C:> \u2022 \n).\\ \n~~~}a \n\nIC3 \n.\", ~~-\" __ ~ __ I 4-_ .. _ .......... _.---_ ... _ ........ -... __ \"\"\"\"\"\"\u00a2t;_-\"'''' .... ~_1 ......... -......,..... \n\nIC4 \n\nIC5 \n\nIC6 \n\n~ ... W\" .... \"1011 ... ~\"_f .... . . \" . , . \" \" '_ /tJ'IfII/'h \n\nI' ...... d1b .. ~*W,.'tJ ...... r' .. ns ... \n\nIC7 \n\nICB \n\nICg \n~._-~.,. . . . . . t . . Wt:n:ePWt.~ .. ,.~I'NJ'~~ \n\nI \n\n10 s \n\nI \n\nFigure 2: Nine independent components found from the MEG data. For each component the \nleft, back and right views of the field patterns generated by these components are shown -\nfull line stands for magnetic flux coming out from the head, and dotted line the flux inwards. \n\n\f", "award": [], "sourceid": 1466, "authors": [{"given_name": "Ricardo", "family_name": "Vig\u00e1rio", "institution": null}, {"given_name": "Veikko", "family_name": "Jousm\u00e4ki", "institution": null}, {"given_name": "Matti", "family_name": "H\u00e4m\u00e4l\u00e4inen", "institution": null}, {"given_name": "Riitta", "family_name": "Hari", "institution": null}, {"given_name": "Erkki", "family_name": "Oja", "institution": null}]}