Artifact cancellation and nonparametric spectral analysis.

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

And then what...And then what...

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