Sparse time artifact removal

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ContentslistsavailableatScienceDirect

Journal

of

Neuroscience

Methods

j ou rn a l h o m epa g e :w w w . e l s e v i e r . c o m / l o c a t e / j n e u m e t h

Basic

Neuroscience

Sparse

time

artifact

removal

Alain

de

Cheveigné

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a_Laboratoire_des_Systèmes_Perceptifs,_UMR_8248,_CNRS,_France b_Département_d’Etudes_Cognitives,_Ecole_Normale_Supérieure,_France c_UCL_Ear_Institute,_United_Kingdom

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•TheSTARalgorithmaddresseschannel-speciﬁcnoisethatissparseintime.

•Itremoveselectrodeorsensornoiseandcertainformsofmyogenicartifact.

•Incontrasttoothertechniques,fewdataarelostandthedimensionalityofthedataispreserved.

•TheSTARalgorithmcomplementscomponentanalysistechniquessuchasICA.

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Articlehistory:

Received25October2015 Receivedinrevisedform 23November2015 Accepted2January2016 Availableonline8January2016

Keywords: EEG MEG LFP ECoG Artifact Myogenic ICA Sensornoise

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Background:MuscleartifactsandelectrodenoiseareanobstacletointerpretationofEEGandother elec-trophysiologicalsignals.Theyareoftenchannel-speciﬁcanddonotfullybeneﬁtfromcomponentanalysis techniquessuchasICA,andtheirpresencereducesthedimensionalityneededbythosetechniques.Their high-frequencycontentmaymaskormasqueradeasgammabandcorticalactivity.

Newmethod:Thesparsetimeartifactremoval(STAR)algorithmremovesartifactsthataresparseinspace andtime.Thetimeaxisispartitionedintoanartifact-freeandanartifact-contaminatedpart,andthe correlationstructureofthedataisestimatedfromthecovariancematrixoftheartifact-freepart.Artifacts arethencorrectedbyprojectionofeachchannelontothesubspacespannedbytheotherchannels.

Results:Themethodisevaluatedwithbothsimulatedandrealdata,andfoundtobehighlyeffectivein removingorattenuatingtypicalchannel-speciﬁcartifacts.

Comparisonwithexistingmethods:Incontrasttothewidespreadpracticeoftrialremovalorchannel removalorinterpolation,veryfewdataarelost.IncontrasttoICAorotherlineartechniques,processing islocalintimeandaffectsonlytheartifactpart,somostofthedataareidenticaltotheunprocesseddata andthefulldimensionalityofthedataispreserved.

Conclusions:STARcomplementsotherlinearcomponentanalysistechniques,andcanenhancetheir abilitytodiscoverweaksourcesofinterestbyincreasingthenumberofeffectivenoise-freechannels.

1. Introduction

Amongthemanysourcesofnoiseandartifactthatplague stud-iesinvolvinghumanand animal electrophysiology, someaffect onlyonechannel atatime. Thispaperaddressessuch channel-speciﬁcartifacts,leavingasideothertypesthatimpingeonseveral channelssuchaseyeblink,heartbeatorbackgroundneural activ-ity.Signalsrecordedbymultichannelrecordingtechniquessuchas electroencephalography(EEG),magnetoencephalography(MEG),

∗ Correspondenceto:Audition,DEC,ENS,29rued’Ulm,75230Paris,France. Tel.:+33144322672/+447912504027.

E-mailaddress:[email protected]

electrocorticography(ECoG),invasiveelectrodearraysoroptical techniquesarerelatedtounderlyingsources byalinearmixing process:

xj(t)=

i

si(t)uij, (1)

where t is time,si(t)are thesourcesignals, and uij are mixing coefﬁcients.Wecall“channel-speciﬁc”a sourcesiforwhichthe uijarezeroforallchannelsjexceptone.

Channel-speciﬁcnoiseincludeselectrodecontactnoise, pulsa-tionnoise,andcertainformsofmuscleartifactinEEG,aswellas sensor noise inMEG or othertechniques.Electrode-tissue con-tactartifactsareusuallytemporallysparse,occurringasisolated events or bursts of events that affect one channel at a time. http://dx.doi.org/10.1016/j.jneumeth.2016.01.005

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Muscleartifactsmayalsobechannel-specificiftheyareproduced bymotorunitsproximaltoasingleelectrode(Yilmazetal.,2014), althoughactivityfromdeepermusclesmayaffectmultiple elec-trodes.Suchartifactsoftenhaveaspectrumthatextendstohigh frequency,buttheymayalsoincludelow-frequencycomponents thatoverlapwithlow-frequencycorticalactivity(Goncharovaetal., 2003),sothatspectralfilteringisnotsufficienttoeliminatethem. Electromyogenicnoiseisparticularlytroublesomeasitcanbe con-fusedwithhigh-frequencycorticalactivity(Yuval-Greenbergetal., 2008;Whithametal.,2007;Muthukumaraswamy,2013;Yilmaz etal.,2014),particularlyasmuscleactivitymaycorrelatewith cog-nitivestate(Whithametal.,2008;Yuval-Greenbergetal.,2008; McMenaminetal.,2011).Cephalicskinpotential(Corbyetal.,1974) mayalsocovarywithcognitivestate,andcontactnoisemay corre-latewithbehavior.

Astandardapproachtodealingwithspatio-temporallysparse artifactsistodiscardeithertheoffendingchannel,orthe offend-ingtimeintervalortrial(Junghöferetal.,2000).Thisentailsloss ofdata,particularlyifartifactsaffectmultiplechannelsand/orare widelydistributedin time,and italsocomplicatesanalysisand interpretationstages,thatneedtobemadetoleranttothemissing data.

Another approach is to apply multichannel linear analysis techniquessuchasindependentcomponentanalysis(ICA), beam-forming,or joint diagonalization (JD) (de Cheveigné and Parra, 2014) to isolate noise components. Component signals yk(t) obtainedbythesemethodsarerelatedtoobservationsas:

yk(t)=

j

xj(t)wjk, (2)

wheretistimeandthewjkareweights.TheJobservationchannels

spanaspacethatcontainsallsuchlinearcombinations,andthe dimensionalityofthedataisthenumberofdimensionsofthisspace (Jor less).Components belongtothisspace.Different methods (PCA,ICA,beamforming,etc.)differinhowtheyﬁndthe appropri-ateweightstoapplytothedata.ICAinparticularhasbeenproposed toremoveartifactsincludingmyogenic(Delormeetal.,2007;Ma etal.,2012;Crespo-Garciaetal.,2008).

Theappealoftheselineartechniquesisthatanoisesourcexi canpotentiallybeperfectlycanceled:acomponentykis insensi-tivetosourceiaslongas

_juijwjk=0,whereuijarethemixing coefﬁcientsandwjkthecomponentweights(Eqs.(1)and(2)).With

high-dimensionaldata(lotsofchannels)thereisconsiderable flex-ibilityin satisfyingthis constraint, and thestrength ofanalysis algorithms suchasICA liesin theirability tofind suchsets of weights.However,ifanoisesourceisspecifictoasinglechannelj, itcanonlybecancelledbysettingwjktozeroforeverycomponent

k,effectivelydiscardingthatchannel.Inthissituation,component analysisofferslittleoverthetime-honoredpracticeofdiscarding noisychannels.

Componentanalysisitselfisvulnerabletochannel-speciﬁcnoise becauseitreliesonthedimensionalityofthedata(determinedby thenumberofchannels)toresolvethevarioussources.Ifchannels arediscardedduetoartifacts,analysismaybeimpaired,whereasif theyarenotdiscarded(duetolackofknowledgeortheneedto con-serveenoughchannels),theartifactisinjectedintotheextracted componentsviaEq.(2).Thepresenceofartifactsmayalsointerfere withtheabilityofthealgorithmtoﬁndtheoptimalwjk.For

exam-pleanalgorithmsuchasCSP(Kolesetal.,1990),thatsearchesfor componentsthatdifferinpowerbetweentwointervals,maylock ontoanartifactthatispresentinoneintervalbutnottheother. Finally,theartifactsmayinterferewiththeabilitytoestimatethe topographyassociatedwithcorticalactivity,possibly compromis-ingsourcemodeling.Channel-speciﬁcnoisethuslimitstheability

oflinearmethodstoimprovethesignaltonoiseratio(SNR)ofweak brainactivity.

Theseconsiderationsleadustofocusonchannel-speciﬁcnoise, leavingothertechniquessuchasICA,JD,orbeamformingtodeal withnoise sourcesthat impinge onmultipleelectrodes.Thisis importantscientiﬁcally,toobtainamoreaccuratepictureofbrain activity,andalsoforapplicationssuchasbrain-computerinterfaces (BCI),predictionofepilepticseizures,wearablebrain-monitoring devices,andsoon.Themethoddescribedhereiseffective,fully automatic,andamenabletoanonlineimplementationfor applica-tionsthatinvolverealtimemonitoring.

2. Methods

2.1. Signalmodelandassumptions

Eachobservationxj(t)isthesumofsignalsfrommultiplesources iwithin thebrainor theenvironment (Eq.(1)).We make sev-eralrestrictiveassumptions. Eachnoisesourceni(t)affectsonly oneparticularchannel(assumption1).Noiseactivityistemporally sparsesothatartifactsondifferentchannelsdo nottemporally overlap(assumption 2), andfor a signiﬁcantproportionof time thedataareartifact-free(assumption3).Finally,weassumethat in theabsence of artifactsthedata are linearlydependent such thateachchannelbelongstothesubspacespannedbytheother channels.Inotherwordsfor eachchanneljthereexista_jj such thatxj(t)=

j₌_/_jajjxj(t)(assumption4).Thisisplausiblefor neu-rogenicactivityduetosource-to-sensormixing.Ofcourse,many kindsofnoisedonotmeettheseassumptions;thefocushereison thosethatdo.Inrealdata,theseassumptionswillbemetonlyas anapproximation,forexamplebecauseofnon-stationarityofthe brainandnoiseprocessesunderlyingthedata.Thequalityofthe outcomedependsonthequalityoftheapproximation.

2.2. TheSTARalgorithm

Thealgorithmproceedsintwophases.Theﬁrstphasedetects thepresenceofchannel-speciﬁcartifacts,thesecondphasecorrects them.

Phase1.Thecovariancematrixofthedataisestimated,and fromitiscalculatedthematrix Athatprojectseachchannelon thesubspacespannedbytheotherchannels.Theprojection ¯xj(t)

ofchanneljistheweightedsumofthechannelsj =/ jthatbest approximatesxj(t).Intheabsenceofanartifactweshouldhave ¯

xj(t)−xj(t)=0asaresultofthelineardependenceassumption,soa

signiﬁcantdeviationindicatesthepresenceofanartifact.Valuesof ¯

xj(t)−xj(t)areﬁtbyazero-meanGaussiandistribution,andvalues

eccentricfromthisdistribution(relativetoapredeﬁnedthreshold )areﬂaggedasartifactual.Thisisrepeatedforallchannels,andthe unionofeccentrictimesamplesislabeledasartifact-contaminated. Thecovariancematrixisinitiallyestimatedfromtheentiredata, andsubsequentlyreestimatedonthepartofdatalabeledas artifact-free.Afewiterationsofthisprocessleadtoastablepartitionofthe timeaxisbetweenartifact-freeandartifact-contaminatedparts.

Phase 2. The artifact-contaminated part is further divided accordingtowhichchannelismostdegradedateachtimesample. Forthispurpose,asecondeccentricitymeasureiscalculatedfor eachchannelastheratioofinstantaneouspowertopower aver-agedovertheartifact-freeportion.Thechannelwiththehighest scoreatagiventimesample“owns”thatsample,anditsdataare replacedwithitsprojectiononthesubspacespannedbytheother channels,usingprojectioncoefﬁcientscalculatedfromthe artifact-freepart.Datareplacementoccursonlyatthepartcorresponding totheartifact:atothertimesthedataareleftintact,somostofthe dataremainuntouchedbytheprocessing.

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-1 0 1 A.U. target (a) -20 0 20 A.U.

mixed with noise (SNR=10) and artifact (b) time -20 0 20 A.U. cleaned by STAR (c) -20 0 20 A.U.

mixed with noise (SNR=10-8) and artifacts (d) -20 0 20 A.U. cleaned by STAR (e) -2 0 2 4 A.U. cleaned by JD (f) time -1 0 1 A.U. cleaned by STAR + JD (g)

Fig.1. Denoisingsimulateddata.(a)Targetsignal.(b)10-channeldataincludingtarget,Gaussiannoise(SNR=10),andanartifactononechannel.Theblackbarindicates STAR’sestimateofthe“artifact-contaminated”part.(c)DataafterremovaloftheartifactbytheSTARalgorithm.(d)10-channeldataincludingthesametargetandGaussian noiseatamuchlowerSNR(10−8₎_and_with_transient_artifacts_on_all_channels._The_black_bars_indicate_STAR’s_estimate_of_the_{“artifact-contaminated”}_part._(e)_Same_after

removalofartifactsbytheSTARalgorithm.(f)ResultofapplyingtheJDalgorithmtotherawdatain(d),withtheaimofrecoveringthetarget.(g)Same,buttheSTARalgorithm wasﬁrstappliedbeforetheJDalgorithm.

2.3. Implementationdetails

AMatlabimplementationofthealgorithmisavailableinthe NoiseToolstoolbox(http://audition.ens.fr/adc/NoiseTools/).Inthe projectionsteps,toavoidissueswithrank-deﬁcientdata,PCAis appliedandPCswithpowerbelowathresholdarediscarded.The algorithm operates ona sample-by-samplebasis, each channel switchingbetweenan artifact-free state(noprojection) and an artifact-contaminatedstate(projection). Tolimitthenumber of switches,theeccentricitymeasureistemporallysmoothedby con-volutionwithashorttriangularwindow.

Thealgorithmthushas4parameters:theeccentricitythreshold (thesamevalueisusedinphases1and2),thesizeofthe smooth-ingkernelinphase2,thenumberofneighborsusedtofixeach channel,andthetruncationthresholdforthePCA.Ofthese,only thefirstiscritical,asitdeterminestheproportionoftime sam-plesthatwillbelabeledasartifact-contaminated.Anexcessively lowthresholdleadstoinsufficient“artifact-free”datatoreliably determineitscorrelationstructure.For convenience,our imple-mentationisdesignedtoautomaticallyincrementthethreshold (byafactor1.1)ifthisoccurs.

Tosavecomputationandreduceoverfitting,channelsmaybe projectedonasubsetofneighbouringchannels,ratherthanonthe fullsetofchannels.Ontheassumptionthatcorticalsourcesof inter-estshouldaffectgroupsofphysicallyclosechannels,thissubset shouldsuffice.‘Neighborhood’canbequantifiedbasedon geomet-ricalproximity,orbymeasuringbetween-channelcorrelationin therawdata.Toimprovenoiserejectionitmaybeusefultoapply STARrepeatedly,sothateachiterationremovesartifactsmissedby thepreviousiteration.

2.4. Relaxingassumption2

Assumption2is oftenviolatedfor myogenicnoise thatmay occurinburstsaffectingmultiplemotorunits(Yilmazetal.,2014). Wecanrelaxittoallowseveralchannels[jC]tobecontaminated, aslongaswemodifyassumption(4)toassumethateachofthe contaminatedchannels[jC]canbeexpressedastheweightedsum

of the remainingnon-contaminated channels. The algorithm is modiﬁedtoprojecteachof[jC] onthesubspacespannedbythe non-contaminatedchannels.Thismodiﬁcationiscomputationally expensive(thenumberofcasestoconsiderisexponentialinthe numberof[jC]),andinourimplementationitisonlyapproximated, seebelow.

3. Results

3.1. Simulateddata

Asinusoidal targetand severalGaussian noise sourceswere

mixed together to simulate multichannel data, and

channel-specificartifactswereadded.Thesinusoidaltargetsignal(Fig.1(a)) wasmixedintothe10-channeldataviaa1×10mixingmatrixwith randomcoefficients,togetherwith8independentGaussiannoise sourcesmixedviaa8×10randommixingmatrix.Coefficientswere chosentoensureSNR=10,andapulse-likeartifactwasaddedto onechannel(Fig.1(b)).ApplyingSTAReffectivelysuppressesthe artifact(Fig.1(c)),apparentlywithoutdistortingthesignal.Thedata remaincontaminatedbytheothernoisesources,althoughatthis SNRthetargetstillemerges.Fig.1(d)showsasimilarmixturewith SNR=10−8 _and_one_artifact_on_each_channel,_and_Fig.₁_(e)_shows theresultofapplyingSTAR.TheblackbarsinFig.1(b,d)indicate STAR’sestimateoftheartifact-contaminatedpart.Theartifactsare removed,butatthisSNRthetargetisinvisible.

AlinearalgorithmsuchasJD(deCheveignéandParra,2014) canbeusedtoextractaweaktargetsuchasFig.1(a)despiteavery unfavorableSNR.Howeverthisrequiresthedimensionalityofthe noisetobesmallerthanthatofthedata,arequirementthatfails inthepresenceofthechannel-specificartifactsinadditiontothe GaussiannoiseasinFig.1(d).Indeed,applyingJDtothe artifact-contaminateddatafailstorecoverthetarget(Fig.1(f)).However, ifSTAR isfirstappliedtoremove theartifacts(Fig.1(e)),JDcan successfullyrecoverthetarget(Fig.1(g)).Thisexampleshowsthat STARcaneffectivelyremovechannel-specificartifacts,thatitcando soforartifactsaffectingmultiplechannels,andthatsuchremoval

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Fig.2.128-channelEEGdata.(a–c)Examplesofsingle-channelsignalsfroma 128-channelEEGrecordingbefore(red)andafter(blue)applyingSTAR.(d)Percentage ofsamplesremovedforeachchannel(sortedbydecreasingpercentage),foreach subject.(e)Proportionofpowerremovedforeachchannel(sortedbydecreasing power),foreachsubject.(Forinterpretationofthereferencestocolorinthislegend, thereaderisreferredtothewebversionofthearticle.)

maybeneededforacomponentanalysistechniquesuchasJDto succeed.

3.2. EEGdata

Afirstexampleinvolvesdatarecordedwitha128-channelEEG system(Biosemi).Thedatasampledat512Hzwerehigh-pass fil-tered with 20Hz cutoff (2nd order Butterworth) to emphasize thegammaregionthat isrelativelysusceptible toartifacts.The STARalgorithmwasappliedwiththresholdparameter=2to sup-presschannel-specificartifacts.Thesizeofthesmoothingwindow appliedtotheeccentricitymeasure was19 samples.Fig.2(a–c) shows three example signals from individual electrodes before (red)andafter(blue)processing.InFig.2(a)thedataare contam-inatedbywhatseemstobemuscleactivity.Thisissuppressedby STAR(thethreeremainingburstsreflectactivitycorrelatedacross sensorsandthereforenotremoved).InFig.2(b)thedataare con-taminatedbyapulsatilenoisewithaperiodofapproximately1s, mostlikelya“pulsationartifact”duetoaveinunderlyingthe elec-trode(NiedermeyerandLopezdaSilva,2005).InFig.2(c)thedata arecontaminatedbyaseriesofglitchesofhighamplitude(notethe scale)thatareequallywellsuppressed.

Data from this study were available for 8 subjects, about 1.5–2.5heach. Fig. 2(d) shows the percentage of samples cor-rectedbySTAR foreachchannel(channelssortedbydecreasing percentage)and subject, cumulated over therecording session. Thepercentagevaries acrosssubjectsandchannels,reﬂecting a differentprevalenceofchannel-speciﬁcartifactsbetweensubjects, andforagivensubject,betweenchannels.Fortheworstsubjectthe percentageisbelow5%formostchannels,implyingthat>95%of thedataofthosechannelswereuntouchedbytheprocessing.For goodsubjectsthepercentageofintactsamplesis>98%foralmost allchannels.Thesenumberssuggestthatthenegativeimpactof applyingSTAR,ifany,islikelytobeminimal.Fig.2(e)showsthe percentageofpowerremovedbySTARforeachchannel(channels

Fig.3. 128-channelEEGdata.(a)Onechannelwithmuscleartifactbefore(red)and after(blue)processing.(b,c)Spectrogramsofthesignalbeforeandafterapplying STAR.(d,e)Same,withsuperimposedchirpsignal,illustratingthatprocessingcan revealasignalotherwisemaskedbytheartifact.(Forinterpretationofthereferences tocolorinthislegend,thereaderisreferredtothewebversionofthearticle.)

sorted by decreasing percentage) and each subject (individual lines).Againthepercentagevariesacrosssubjectsandchannels.For theworstsubject,>20%ofpowerwasremovedfor>30channels, and>55%fortheworstchannel.Forothersubjectsthe percent-agesaresmaller,butstillsignificantforasubsetofchannels.To summarize,STARisbothsafeandofpotentiallysignificantbenefit. Fig.3(a)showsonechannelcontaminatedbyaburstofpulsatile activity,likelymuscleartifact,before(red)andafter(blue)applying STAR.ThespectrogramofthesedataisshowninFig.3before(b), andafter(c)processing.Artifactualactivitydominatesthehigher spectralregion,butthisisalleviatedbyprocessing.Fig.2(d)and(e) illustrateshowthisprocessingcouldpotentiallyrevealhigh fre-quencyactivity(hereasynthesizednarrowbandchirp)otherwise maskedbytheartifact.

Asecondexampleusesdatarecordedfromthreeclosely-spaced EEGelectrodeswithintheearcanalofasubject(Kidmoseetal., 2012).The rationaleforrecording fromwithintheear is unob-trusiveness (for hearingaid-related applications) and the hope thatmuscleartifactswillbeweaker,however theclosespacing betweenelectrodesisexpectedtoresultinsignalshighly corre-latedacrosschannels.Fig.4(a)showsashortsegmentofsignals fromthethreeelectrodes.Contrarytoexpectations,onechannel (green)isaffectedbychannel-specific glitchesof possible mus-cularorigin.ApplyingSTAR removestheseartifactsresultingin signalsthataremuchmoresimilaracrosschannels,asexpected fromcollocatedelectrodes(Fig.4(b)).Anotherwaytoattenuate channel-specificartifactsistoaverageacrosschannels,butthe ben-efithereisrelativelysmall(Fig.4(c),red).HoweverapplyingSTAR beforeaveraginggreatlyincreasesthisbenefit(blue).Thedeflection near0.5sisnotremovedbecauseitissharedacrosssensors.The effectofartifactreductionofthe3-channeldataisreflectedinits PCAspectrum(Fig.4(d)).Corticalsignalsfromcloselyspaced elec-trodesshouldbehighlycorrelated,implyingarapidlydecreasing PCAspectrum,andthisexpectation isbettermetafterapplying STAR.ThisexampleshowsthatSTARcanbeeffectiveevenfora smallnumberofchannels.

3.3. SimulatedtargetembeddedinrealEEG

This example involves a simulated repetitive target (half-sinusoidpulse)superimposedonthesame3-channelEEGsignal asinthepreviousexample.Theadvantageofusingasimulated targetisthatthegroundtruthisknown,theadvantageofusing realEEGasnoiseisthatitisrepresentativeofrealEEGnoise.The

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0 0.5 1 1.5 2 s -200 0 200 V raw (a) 0 0.5 1 1.5 2 s STAR (b) 0 0.5 1 s -100 -50 0 50 100 V

average over channels

(c) raw STAR 1 2 3 PC 0.001 0.01 0.1 1 power (d) raw STAR 0 1 norm. amplitude raw (e) 0 1 norm. amplitude

cleaned with STAR (f) 0 0.5 1 s 0 1 norm. amplitude cleaned with JD (g) 0 0.5 1 s 0 1 norm. amplitude

cleaned with STAR + JD (h)

Fig.4.Three-channelEEG.(a)Rawdata.(b)SameafterartifactremovalbySTAR.(c) Averageoverchannelsofraw(red)orprocessed(blue)data.(d)Eigenvalue spec-trumofraw(red)andprocessed(blue)data.ThesmallerpowerofPCs2and3 indicatesthatthesignalsareclosertobeingidenticalacrosschannels,asexpected forthreecollocatedelectrodes.(e,f)Simulatedtarget(290repetitionsofa half-sinusoid)embeddedin3-channelEEGnoise(SNR=0.03).Blueisaverageovertrials, graybandindicates±2SDofabootstrapresamplingofthemean.(e)Averageover trialsofthe“best”electrode.(f)Sameas(e)afterapplyingtheSTARalgorithmto sup-pressartifacts.(g)Sameas(e)afterapplyingtheJDalgorithmtoenhancethetarget. (h)Sameas(e)afterapplyingﬁrstSTARthenJD.Thevaluesplottedarenormalized toequatethevarianceovertrialsineachcondition,thusthegreateramplitudeofthe mean(blue)in(h)reﬂectsthebetterSNRoftherecoveredsignal.(Forinterpretation ofthereferencestocolorinthislegend,thereaderisreferredtothewebversionof thearticle.)

targetpulsewasrepeated290timesandaddedtothesecond chan-neloftheEEGwithSNR=0.03.Fig.4(e)showstheaverageover trialsofthesecondEEGchannel.Thegraybandrepresents±2SD ofabootstrapresamplingofthemean.Thepresenceofartifactsis reflectedbytheirregularwidthofthegrayband.Inprinciple,the SNRofsuchmultichanneldatacanbeenhancedbytheJD algo-rithm(deCheveigné andParra,2014)withtheappropriatebias functiontoenhancerepeatablecomponents.Howeverinthiscase thebenefitislimited(Fig.4(g))presumablybecauseallchannels areartifact-contaminatedsothatthereisnoartifact-freesubspace. ApplyingtheSTARalgorithmattenuatestheseartifacts(Fig.4(f)) andJDproducesawell-isolatedtargetsignal(Fig.4(h)).This exam-pleshowsagainthatremovingchannel-specificartifactswithSTAR canimprovetheeffectivenessofcomponentanalysis.

4. Discussion

TheSTARalgorithmexploitsthebetween-channelcorrelation oftheunderlyingdatatoidentifychannel-specific artifactsand repairthem.Figuratively,it“surfs”thecorrelationstructureofthe underlyingdata,selectively shavingoffthepartsthatdonotfit. Channel-specificartifactsareubiquitousinEEGandotherrecording techniques.Removingthemisusuallytedious(ifdonemanually)

orcomplexandunreliable(ifdoneautomatically),andareliable automaticmethodtosuppressthemisthususeful.

4.1. Comparisonwithotherapproaches

Themostcommonapproachtochannel-speciﬁcartifactsisto discardtheoffendingchannel(s),orelsetheoffendingsamplesor trials(Pictonetal.,2000).Validdataarelostasaresult,andthe strategyfailsiftoomanychannelsand/orsamplesareaffected. Incontrast,STARentailsminimaldataloss,becauseonlyasmall proportionofsamplesarediscarded.Dataarerejectedona sample-by-samplebasis,incontrastforexampletoSCADS(Junghöferetal., 2000)thatremoveslargerchunks(trials)oftheaffectedchannel,or AFOP(Boudetetal.,2012)thatoperatesonarelativelylongwindow (e.g.20s).

Asinseveralotherapproaches,missingchannelsare interpo-latedspatially.InSTARtheinterpolationisbasedonanestimate ofthecorrelationstructuregatheredovertheartifact-freepart,in contrasttomethodssuchasSCADSthatapplysphericalspline inter-polationtoreconstructthemissingdata(Perrinetal.,1989).STAR thusrequiresnogeometricalinformation(itispurelydata-driven) althoughitmaybeneﬁtfromusingaproximitymaptorestrictthe numberofchannelsuponwhicheachchannelisprojected.STAR usesthemultivariatecorrelationstructureofthedata,incontrast towaveletorempiricalmodebasis(Saﬁeddineetal.,2012)thatuse thewithin-channelautocorrelationstructuretointerpolatemissing values.

Averydifferentapproachistousecomponentanalysistoform linearcombinationsofchannelsasinEq.(1),andprojectthe com-ponents that correspondto artifactsout of thedata. Thereare manytechniquesavailable(ICA,beamforming,JD,etc.)that dif-ferinthewaytheydeterminetheweightswjk.InICA(Delorme

etal.,2007;Maetal.,2012;Crespo-Garciaetal.,2008)ameasure ofstatisticalindependence(e.g.kurtosis)isusedtoconstrainthe weights.Channel-specificnoiseisusuallybothkurtotic(lotsofzero orextremevalues)andindependentbetweenchannels,sothis pro-cedureislikelytoisolatecomponentsthatcontainchannel-specific noise.Inbeamforming(Grosse-Wentrupetal.,2009)aspatialfilter isusedtoisolatesources,eitherdesired(toextractthem)or unde-sired(tosuppressthem),onthebasisoftheirspatialposition.InCSP (Kolesetal.,1990)orJD(deCheveignéandParra,2014)thespatial filterisinsteaddesignedtomaximizeorminimizesomedesirable orundesirabletraitofthedata.

Regardlessofthemethod,componentanalysisfacesa funda-mentallimitation:itcannotresolvemoresourcesthandimensions inthedata.STARisnotsubjecttothislimitation,asillustratedby theexampleinFig.1(d–g)whereartifactswerepresentonall chan-nels,inadditiontotargetandnoisesources,butthetargetcould nonethelessbeseparated.NeitherICA,norJD,norbeamformingcan dealwiththissituationbecausethenumberofsourcestoresolve exceedsthenumberofchannels.ThereasonwhySTARsucceedsis thatitoperateslocallyintime(sothatthesolutionappliedtoﬁx eachsampleneednotconsiderothersamples),andleavesmostof thedataintact(thedimensionalityofthecleaneddataisthatof thedatabeforeartifactswereadded).Incontrast,techniquessuch asICAapplyasinglelineartransformtoallthedata,eachartifact removedreducesthedatadimensionality,andtheremaynotbe enoughdimensionstoallowthemalltoberemoved.Asstressed inSection1,anartifactspeciﬁctochanneljcanonlyberemoved bysettingallthewjktozeroinEq.(2),i.e.discardingthat

elec-trode,andthereforeifartifactsarepresentonmanychannelsthe dimensionalityisgreatlyreduced.Empirically,theeffectivenessof ICAasa tooltoreduce myogenicartifactshasbeenquestioned because ICs may be found to contain both artifact and neural activity(McMenaminetal.,2010,2011),presumablyasa conse-quenceofthelargenumberofdistinctgeneratorsofmuscleartifact.

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SimilartoSTAR,thesensornoisesuppression(SNS)method(de CheveignéandSimon,2008b)addressessensor-speciﬁcnoiseby replacingeachchannelbyitsprojectiononthesubspacespanned bytheotherchannels.HoweverwithSNSthisoperationisapplied uniformlyacrossthetimeaxis,andthussharesthesamedrawbacks ofothercomponentanalysistechniques.

TheAFOPmethodofBoudetetal.(2012)appliesdifferent solu-tionstodifferentpartsofthetimeaxis(ortime-frequencyplane). Artifacts withina limited spectrotemporalwindow areisolated using a variantof the commonspatial pattern (CSP) algorithm (Kolesetal.,1990),andthedataoverthatwindowarefixedby projectingthemout.AFOPcanremoveanyactivityspecifictothat window,notjustchannel-specific,incontrasttoSTARwhichonly removeschannel-specificartifacts.Howeverasnotedabove,AFOP operatesatacoarsertemporalgranularity.

ThefocusofSTARonchannel-speciﬁcartifactscouldbeseen asalimitation.Howeverthisrestrictionallowsittoavoid remov-ingactivitysharedacrosschannels,ofdeeperandpossiblyneural origin. Most importantly, STAR is compatible with other tech-niques(ICAorother)thatcandealwithchannel-sharedartifacts, increasing their effectiveness by relieving them of the burden ofchannel-speciﬁc artifacts.Indeed,theprimary motivationfor developingSTARwastopushthelimitsofthesenoisereduction techniques,includingourownpreviousefforts(deCheveignéand Simon,2007,2008a,b;deCheveigné,2010,2012;deCheveignéand Parra,2014).

AnfeatureofSTARisthatitisautomatic,incontrastto tradi-tionalartifactrejectionthatrequires manualintervention,orto ICAthat requiresinspectionof componentsto decidewhichto remove.Itisrelativelyparameter-free,incontrasttomethodssuch asFASTER(Nolanetal.,2010)thatinvolvemultipleparameters.It isalsoconceptuallysimpleandcomputationallyfast.

Tosummarize themainfeatures that distinguishSTARfrom otherapproaches:(a) itis automatic andrequires little tuning, (b) dimensionality is not reduced and apart from the artifact portionsthedataareuntouched,(c)themethodaddressesonly channel-speciﬁcartifacts,leavingotherformsofartifacttoother approaches,thatitcomplementsandcanenhance.

4.2. Caveatsandcautions

Assumption4requiresthatthedimensionalityoftheactivity underlyingthedata(e.g.numberofsigniﬁcantneuralsources)be lessthanthenumberofchannels.Astherearepotentiallybillions ofneuralsourcesthiscanonlybeanapproximation.

Thecorrelationstructure isassumedtobestationarysothat theprojectionparameters estimated fromthe artifact-free part canbeappliedintheartifact-contaminatedpart.Adeparturefrom thisassumption(forexampleifadditionalneuralsourcescoincided withmuscleartifact)wouldreduceeffectiveness.

Thecalculationoftheprojectionmatrix,thatallowseach chan-neltobereplacedbyitsprojectionontheotherchannels,issubject tooverﬁttingifthereisalargenumberofchannelsorinsufﬁcient data.Itisusefultolimittheprojectiontoasubsetofneighboring channels(10seemstoworkwell).

Assumptions2and3requirethatchannel-specificartifactsbe localintime,which excludesslowchannel-specificfluctuations. Itmaybeusefultoremovesuchslowfluctuationsbyhigh-pass filteringthedatabeforeapplyingSTAR(orsplitthedatainto low-andhigh-passstreams,processthelatter,thenrecombine).

Foreachchannel,thealgorithmswitchesbetweenan artifact-free state, for which the data are untouched, and an artifact-contaminated state for which the data are replaced by their projection.Thetransitionbetweenstatesmayproduceastep,and thismayparadoxicallyleadtoincreasedhigh-frequencynoiseif thetransitionsarenumerousand/orthestepsarelarge.Smoothing

theeccentricitymeasurereducesthenumberofswitches,andin practiceswitchingseemsrarelyaproblemunlessthedatacontain alotoflow-frequencypower(seepreviouspoint).

Assumption2,thatartifactsshouldoccurononlyonechannel atatime,isoftenviolatedformyogenicactivitythatmayoccur inburststhataffectseveralchannelssimultaneously.Thishastwo consequences.First,thealgorithm(initsbasicform)onlyﬁxesone channelatagiventimepoint,andsoartifactsontheotherchannels mayremain.Second,projectiononartifact-contaminatedchannels maycontaminatethechannelbeingﬁxed.Theextensiondescribed inSection 2.4addressestheproblem,althoughitsapplicabilityis limitedbythecomputationalcostofdealingwiththemany com-binationsofartifact-contaminatedchannels(exponentialintheir number).TheNoiseToolstoolboximplementsanapproximation thatappearstobeeffective.STARmaybeappliedrepeatedly,so thateachnewpassremovesartifactsmissedbypreviouspasses. 4.3. Applicabilitytoelectromyogenicactivity

ThereisevidencethatmuchEEGpowerbeyond20Hzis mus-cularin origin: when muscular activityis silencedby injection of a paralysingdrug, powerin that bandis greatly diminished (Whithamet al.,2007).Thefact thatmuscularactivitycovaries withmentalstatemakesitapotentialconfoundincognitive stud-ies(Whithametal.,2008;Yuval-Greenbergetal.,2008;Shackman etal.,2009).TheSTARalgorithmoffersapartialsolution,inthatit removesthetypeofmyogenicactivitythatislocaltoone elec-trode (Ma et al., 2012).This constitutes a subset of myogenic activity:activitythatisinsteadcorrelatedacrosselectrodes(e.g. fromdeeperordistantmuscles)mustberemovedbyothermeans (McMenamin et al.,2010; Yilmaz et al.,2014).Empirically, the amountofreductionobservedforeachartifactburstisvariable, rangingfrom100%toafewtensofpercent(e.g.Fig.3).Artifactsthat arecorrelatedacrosselectrodes(e.g.fromocularordeepmuscles) maybeaddressedbycomponentanalysissuchasICAorJD,towhich STARiscomplementaryinthatitavoidssquanderingdimensions usefultothosemethods.TheSTARalgorithmisthusofpotential beneﬁtinstudiesofcorticalactivityathigherfrequencies. 4.4. Applicabilitytoreal-timeandBCIapplications

Thealgorithmcanoperateonlineinrealtime.Afteraninitial bootstrapphase(togetanestimateoftheartifact-freecovariance matrix),thealgorithmswitchesbetweentwostates:(1)noartifact, thecovariancematrixisupdated,(2)artifact,theoffending chan-nelsarecorrected.Updatingofthecovariancematrixestimatemay occurforexampleaccordingtoaleakyintegratormechanism,to allowforslowvariationsofthecorrelationstructure.

ApplicationssuchasBCIinvolvingawearableEEGdeviceare limitedby artifactsrelated tomovement,includingcontactand muscleartifacts(Fatourechietal.,2007;McFarlandetal.,2005; Reisetal.,2014)thatcanforexampledisruptanotherwise effec-tivetechniquesuchasCSP(Grosse-Wentrupetal.,2009).Manual correctionorofﬂineprocessingareobviouslyruledout,andSTAR thusisofpotentialbeneﬁtfortheseapplications.

5. Conclusions

Thesparsetimeartifactreduction(STAR)algorithmdeals effec-tively with channel-speciﬁc artifacts that are common in EEG, includingelectrodecontactnoiseandcertaintypesofmuscle arti-fact.Itoperateslocallyintime,correctingonlythesamplesaffected bytheartifact,andleavingtheremainderintact,andthushas min-imalnegativeimpactontheunderlyingdata.Removalofanartifact doesnotreducethedimensionalityofthedata,incontrastto chan-nelrejectionorcomponentanalysistechniquessuchasICA.The

(7)

STARalgorithm cancomplementthose techniquesand enhance theireffectivenessbyrelievingthemoftheburdenofdealingwith channelspeciﬁcartifacts.TheSTARalgorithmoperates automati-cally,requiresfewparameters,iscomputationallyefﬁcient,andcan beimplementedtoperformonlineprocessinginrealtime.

Acknowledgements

ThisworkwassupportedbytheEUH2020-ICTgrant644732

(COCOHA),andgrantsANR-10-LABX-0087IECand

ANR-10-IDEX-0001-02 PSL*. Ed Lalor and Giovanni Liberto contributed the 128-channelEEGdata,andThomasLunnerandCarinaGraverson contributedthe3-channelEEGdata.

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