Artifact cancellation and Artifact cancellation and nonparametric spectral nonparametric spectral
analysis analysis
OutlineOutline
Artifact processingArtifact processing Artifact cancellationArtifact cancellation Nonparametric spectral analysisNonparametric spectral analysis
IntroductionIntroduction
Artifact processingArtifact processing RejectionRejectioncancellationcancellation Rejection main alternativeRejection main alternative
• one would hope to retain dataone would hope to retain data Cancellation requirementsCancellation requirements
• clinical informationclinical information• no new artifactsno new artifacts• spike detectorsspike detectors
Additive/multiplicative modelAdditive/multiplicative model Artifact reduction using linear filteringArtifact reduction using linear filtering
Artifact cancellationArtifact cancellation
Using linearly combined reference signalsUsing linearly combined reference signals Adaptive artfact cancellation using linearly Adaptive artfact cancellation using linearly
combined reference signalscombined reference signals Using filtered reference signalsUsing filtered reference signals
Linearly combined reference Linearly combined reference signalssignals
Eye movements & Eye movements & blinksblinks several referene several referene
signalssignals positioningpositioning additive modeladditive model EOG linearly EOG linearly
trasferred to EEGtrasferred to EEG• weightsweights
In detailIn detail
UncorrelatedUncorrelated Mean square errorMean square error Minimization, differentationMinimization, differentation Spatial correlation, cross correlationSpatial correlation, cross correlation
fixed over timefixed over time zero gradientzero gradient
EstimationEstimation blinks, eye-movements at onsetblinks, eye-movements at onset
In detail 2In detail 2
Number of reference signalsNumber of reference signals Only EOG cancelledOnly EOG cancelled ECGECG Rejection used a lot (in MEG)Rejection used a lot (in MEG)
expect when lots of blinks (ssp)expect when lots of blinks (ssp)
Adaptive versionAdaptive version
Time-varying changesTime-varying changes Tracking of slow changesTracking of slow changes Adaptive algorithmAdaptive algorithm
LMSLMS weight(s) function of timeweight(s) function of time
• optimal solution changes with timeoptimal solution changes with time method of steepest descentmethod of steepest descent negative error gradient vectornegative error gradient vector
In detailIn detail
Parameter selectionParameter selection timetime noisenoise
ExpectationExpectation instantaneous valueinstantaneous value zero settingzero setting performance performance
estimationestimation fluctuation of weightsfluctuation of weights
Filtered reference signalsFiltered reference signals
EOG potentials exhibit frequency EOG potentials exhibit frequency dependencedependence in trasfer to EEG sensor through tissuein trasfer to EEG sensor through tissue blinks and eye movementsblinks and eye movements
Improved cancellation with transfer Improved cancellation with transfer function replacementfunction replacement spatial and temporal informationspatial and temporal information vv00 estimation estimation FIR (lengths)FIR (lengths)
DetailsDetails
Stationary processes Stationary processes Second order characterisricsSecond order characterisrics Correlation information fixed Correlation information fixed
Details 2Details 2
No No a prioria priori information information can be implemented, modified errorcan be implemented, modified error
Also adaptive version existsAlso adaptive version exists a prioria priori impulse responses calculated at impulse responses calculated at
calibrationcalibration
Nonparametric spectral analysisNonparametric spectral analysis
Richer characterization of background Richer characterization of background activity that with 1D histogramsactivity that with 1D histograms
EEG rhythmsEEG rhythms Correlate signals with sines and cosinesCorrelate signals with sines and cosines When?When?
Gaussian stationary signalsGaussian stationary signals• Stationary estimatationStationary estimatation
Normal spontaneous waking activityNormal spontaneous waking activity
Nonparametric 2Nonparametric 2
Fourier-based power spectrum analysisFourier-based power spectrum analysis no modeling assumptionsno modeling assumptions
Spectral parametersSpectral parameters interpretationinterpretation
Fourier-based power spectrum Fourier-based power spectrum analysisanalysis
Power spectrum characterized by Power spectrum characterized by correlation function (stationary)correlation function (stationary) If ergodic, approximate with time average If ergodic, approximate with time average
estimator (negative lags)estimator (negative lags) combination called periodogramcombination called periodogram equals squared magnitude of DFTequals squared magnitude of DFT
Fourier considerationsFourier considerations
Periodogram biasedPeriodogram biased window dependent (convolution)window dependent (convolution) smearing (main lobe)smearing (main lobe) leakage (side lobes)leakage (side lobes)
• synchronized rhythm better described by power in synchronized rhythm better described by power in frequency bandfrequency band
variance periogoramvariance periogoram• does not approach zero with sample increasedoes not approach zero with sample increase
consistencyconsistency
PeriodogramPeriodogram
Windowing and averagingWindowing and averaging leakage & periodogram variance reductionleakage & periodogram variance reduction
WindowsWindows from rectangular to smaller sidelobesfrom rectangular to smaller sidelobes
• wider main lobe, spectral resolutionwider main lobe, spectral resolution
Variance reductionVariance reduction nonoverlapping segments, averagingnonoverlapping segments, averaging
• resolution decrease, trade-offresolution decrease, trade-off• combinations, degree of overlapcombinations, degree of overlap
Spectral parametrsSpectral parametrs
Resulting power spectrum often not Resulting power spectrum often not readilty interpretedreadilty interpreted Condensed into compact set of parametersCondensed into compact set of parameters feature extractionfeature extraction
• parameters describing prominent features of the parameters describing prominent features of the spectrumspectrum
peaks, frequencies peaks, frequencies
• general usagegeneral usage
Spectral choicesSpectral choices
Visual inspectionVisual inspection format selectionformat selection assessing represantivenessassessing represantiveness
ScalingScaling scope of the analysisscope of the analysis
ParametersParameters
Power in frequency bandsPower in frequency bands Peak frequencyPeak frequency Spectral slopeSpectral slope Hjort descriptorsHjort descriptors Spectral purity indexSpectral purity index
Power in frequency bandsPower in frequency bands
Fixed/statistical bandsFixed/statistical bands alpha, beta, theta etc.alpha, beta, theta etc. from datafrom data
Ratio of, absolute powerRatio of, absolute power comparison, nonphysiological factorscomparison, nonphysiological factors
Peak frequencyPeak frequency
Frequency, amplitude, widthFrequency, amplitude, width ad hocad hoc methods for determining peaks methods for determining peaks more than just maximum more than just maximum
median, meanmedian, mean
Spectral slopeSpectral slope
EEG activity made of 2 componentEEG activity made of 2 component rhythmic, unstructuredrhythmic, unstructured
Based on decay of high frequency Based on decay of high frequency componentscomponents one parameters approximationone parameters approximation
• least squares errorleast squares error
Quantifcation of EEGQuantifcation of EEG Preconditioning of power estimatePreconditioning of power estimate
Hjort descriptorsHjort descriptors
Spectral momentsSpectral moments HH00 (activity) (activity) HH11 (mobility) (mobility) HH22 (complexity) (complexity)
Signal power, Signal power, dominant frequency, dominant frequency, bandwidthbandwidth
Effectively in time Effectively in time domaindomain
Clinically usefulClinically useful
Spectral purity index (SPI)Spectral purity index (SPI)
HeuristicHeuristic Reflects signal bandwidth (HReflects signal bandwidth (H22))
How well signal is described by a single How well signal is described by a single frequencyfrequency noise susceptibilitynoise susceptibility
SummarySummary
Artifact cancellationArtifact cancellation reference signalsreference signals linear combinations, filteringlinear combinations, filtering
• adaptive version(s)adaptive version(s)
Spectral parametersSpectral parameters nonparametricnonparametric
• no modellingno modelling parametricparametric
• interpretationinterpretation
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