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xLXRX4PxlassicalPLOR/TXPXnalysisPRecursivelyPXppliedTodorPVordanov]GPKarstenP@oechstetter].GPPatrickP9erg]FGP)sabellaPPaulmVordanov]GPMichaelPScherg]
MunichPUniversityPofPXppliedPSciencesGPMunichGP(ermany.
9/SXP(mb@GP(räfelfingGP(ermany]
UniversityPofPKonstanzGPKonstanzGP(ermanyF
[]]PXndersonGPVäSäGP_ergusonGPMäXäGPLopezmLarsonGPMäGPYurgelunmToddGPqäGP.[]]äPReproducibilityPofPSinglemSubjectP_unctionalPxonnectivityPMeasurementsäPXmäPVäPNeuroradioläPF.GPDYN–DDDä[.]PLinGP_äm@äGPWitzelGPTäGPXhlforsGPSäPäGPStufflebeamGPSäMäGP9elliveauGPVäWäGP@ämäläinenGPMäSäGP.[[0äPXssessingPandPimprovingPthePspatialPaccuracyPinPM/(PsourcePlocalizationPbyPdepthmweightedPminimummnormPestimatesäPNeuro)magePF]GP]0[–]j]äP[F]PLiuGP@äGP(aoGPXäGPSchimpfGPPä@äGPYangGP_äGP(aoGPSäGP.[[YäPXPrecursivePalgorithmPforPthePthreemdimensionalPimagingPofPbrainPelectricPactivity4PShrinkingPLOR/TXm_OxUSSäP)///PTransäP9iomedäP/ngäPD]GP]j5Y–]N[.ä[Y]PMaddockGPRäVäGP(arrettGPXäSäGP9uonocoreGPMä@äGP.[[]äPRememberingPfamiliarPpeople4PthePposteriorPcingulatePcortexPandPautobiographicalPmemoryPretrievaläPNeuroscienceP][YGP00j–0j0ä[D]PPascualmMarquiGPRäqäGPMichelGPxäMäGPLehmannGPqäGP]55YäPLowPresolutionPelectromagneticPtomography4PaPnewPmethodPforPlocalizingPelectricalPactivityPinPthePbrainäP)ntäPVäPPsychophysioläPOffäPVäP)ntäPOrganäPPsychophysioläP]NGPY5–0Dä[0]PSkrandiesGPWäGP]55DäPSourcePlocalization4PxontinuingPqiscussionPofPtheP)nversePProblemäP)S9/TPNewsläP0ä[j]Phttp4zzwwwäbesaädezupdateszbesa_simulatorz
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TodorPVordanovPMtodoräjordanov7besaädeS(räfelfingGP(ermany
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Real EEG dataDatavwerevacquiredvinvanvauditoryvoddballvexperimentvwithv-AAvHzvstandardvtonesvf‘%Pvrepetitions4vandv-%AvHzvdeviantvtonesvf1G‘vrepetitions4OvpresentedvtovthevsubjectvthroughvthevrightvearEvForvthevmethodvcomparisonOvlocalizationvwasvperformedvatv‘Pvmsvpostvstimulusvinvthevaveragedvresponsevtovthevstandardvstimulivf-k-vtrialsvaftervartifactvrejection4ECLARAInvanvinitializationvstepOvavLORET'vimagevisvcalculatedEvThenvthevfollowingvstepsvarevperformedvperviterationSvvvvvvvv:EvThevresultingvimagevisvspatiallyvsmoothedvwithvavGDvGaussianvkernelvfthisvstepvisvvvvvvvvvvvvvomittedvinvthevfirstviteration4Evvvvvvvv1Ev'llvgridvpointsvwithvamplitudesvbelowvavthresholdvofv:gvofvthevmaximumvactivityvarevvvvvvvvvvvvvsetvtovzeroOvthusvbeingveffectivelyveliminatedvfromvthevsourcevspacevinvthevsubsequentvstepEvvvvvvvvGEvThevresultingvimagevdefinesvavspatialvweightingvtermvfforveachvvoxelvthevcorrespondingvimagevamplitude4EvvvvvvvvkEv'vLORET'vimagevisvcomputedvwithvanvadditionalvspatialvweightingvtermvforveachvvoxelvasvcomputedvinvstepvGEThevprocedurevcanvbevrepeatedvonevorvmorevtimesvdependingvonvthevdatavandvthevresearchvobjectivesEComparison procedureParametersvusedvforvcomparingvthev iterativevmethodsvwerevthevdistancevtovthevsimulatedvsourcesOvandvthevnumbervofv thevestimatedvsourcesvfnumberv ofv maximav inv thev volumev distribution4Ev Thev threev methodsv thatv werev comparedv werev f:4v 7L'R'v Rv applyingv depthv weightingv andvLaplacevweightingvforveachviterationOvf14v‘SLF’vRvavmodifiedvalgorithmvwithvdepthvweightingvbutvwithoutvLaplacevweightingvduringvtheviterationsvfcomparablevwithvShrinkingvLORET'RFO7USSv[G]4vandvfG4v‘LaplacevonlyvfLO4’vRvanothervmodificationvwithoutvdepthvweightingvbutvwithvLaplacevweightingvduringvtheviterationsEvThevcomparisonvwasvperformedvforvregularizationvvaluesvAEAAA:OvAEA:OvAE:OvAE%vfgvofvthevlargestvsingularvvaluevforvthevMooreRPenrosevpseudoinversevcalculation4vandvnumbervofviterationsv1Ov%Ov:AE
Data with different SNRsThev bestv resultsv forv thev datav withv differentvSNRsv wereSv 7L'R'v Rv %v iterationsOv AEA:vregularizationOv thev samev forv thev iterationsvweightedv onlyv withv Laplacev andv SLFv Rv %viterationsOvAE%vregularizationvfFigurevG4E
Fig. 2P xomparisonP betweenP LOR/TXP andP xLXRXP forPclosembyP deepP sourcesäP TheP dipolesP markP theP simulatedPsourcesPMleftSGPthePestimationPwithPLOR/TXPisPshownPinPthePmiddleGPthePestimationPwithPxLXRXPonPthePrightäP
Fig. 3PResultsP forP thePdifferentP iterativePmethodsäPThePbluePandPgreenPlinesPshowPthePdistancePtoPthePsimulatedPsourcesPinP mmäP TheP redP andP purpleP linesP denoteP theP numberP ofPestimatedPsourcesä
Application to real EEG data'pplicationv ofv 7L'R'v tov realv EEGv datavrevealedv thev expectedv activityv inv bothvauditoryvcorticesvfFigurevk4E
Fig. 4P SourceP reconstructionP withP xLXRXP MleftSGP LOPMmiddleSP andP SL_P MrightSäP ResultsP areP comparableP forP allPthreeP methodsäP ResultsP calculatedP withP SL_P shiftP theP leftPsourcePfurtherPsuperiorPthanPthePotherPtwoPmethodsä
Simulation LOR/TX xLXRX xLXRX LaplacePonly SL_
Fig. 1PSimulationsPwithPdifferentPlevelsPofPnoiseP
NoPnoise
OnlyPnoise SNRP.
SNRP5 SNRP.[
R LR L
Lowv resolutionv electromagneticv tomographyv fLORET'4v [%][P]v isv av wellv knownv methodv forv sourcev reconstructionv basedv onv thev weightedvminimumvℓ1Rnormvalgorithmv[1]vwithvthevinversevLaplacevoperatorvasvanvadditionalvweightingvtermEvEvenvthoughvitvwasvshownvthatvthevmethodvlocalizesv deepv sourcesv correctlyOv itv appearsv tov producev av veryv smoothv andv widespreadv sourcev distributionOv andv failsv tov resolvev closelyvneighboringvcorticalvsourcesEvInvordervtovovercomevthesevdifficultiesOvavnewviterativevapplicationvofvLORET'vwithvavreducedvsourcevspacevperviterationvisvsuggestedEvThisvmethodvisvcalledv7lassicalvLORET'v'nalysisvRecursivelyv'ppliedvf7L'R'4E
Resultsvdemonstratevthatv7L'R'S➤vEEEvisvablevtovlocalizevdeepvsourcesvcorrectlyO➤vEEEvisvablevtovresolvevcloselyvneighboringvsourcesO➤vEEEvyieldsvfocalvlocalizationsO➤vEEEvperformsvreliablyvovervavwidevrangevofvnoisevlevelsvand➤vEEEvreliablyvestimatesvthevactivityvinvrealvEEGvdatavacquiredvvvvvundervthevconditionvofvanvauditoryvoddballvexperimentEv
➤v Inv orderv tov investigatev 7L'R'’sv andv LORET'’sv abilityv tov resolvev sourcesv thatv arev closevtogetherOv twovcloselyvneighboringvdipolesv fFigurev14vwithoutvnoisevwerevsimulatedv inv thev leftvandvrightvdorsalvposteriorvcingulatevareavG:v[:][k]E➤v Tov comparev 7L'R'v withv otherv iterativevmethodsOv brainv activityv wasv simulatedv inv thev leftv andvrightvHeschlFsvgyrusEvRealvEEGvnoisevwasvaddedvtovthevsimulatedvevokedvresponsesvresultingvinv:1vdifferentvsignalRtoRnoisevratiosvfSNRs4vbetweenv1vandv1AvfFigurev:4E➤vDatavwerevgeneratedvwithvthevfreevtoolvBES'vSimulatorv[C]E
Simulations
CLARA vs. LORETAThev simulationv withv neighboringv sourcesvshowedv thatv LORET'v wasv notv ablev tovresolvev thev sourcesv evenv withv thev minimumvregularizationv possibleEv 7L'R'v localizedvbothvsourcesvcorrectlyvwithvavregularizationvofvAEAAA:vandv:AviterationsvfFigurev14E
FuturevdevelopmentsS➤v 7orticalv 7L'R'Sv Restrainingv thev solutionv tov thev corticalv surfacev andvapplyingv av 1Dv insteadv ofv GDv Laplacianv wouldv improvev thev methodv withvrespectvtovthevfollowingvtwovaspectsE:EvThevGDvLaplacianvsmoothsvinvallvthreevdirectionsvwithoutvaccountingvforvthevcorticalvtopologyE1EvThevGDvLaplacianvisvunstablevonvthevbrainvboundaryE