Artifact cancellation and nonparametric spectral analysis

Outline  Artifact processing  Artifact cancellation  Nonparametric spectral analysis

Introduction  Artifact processing Rejection  cancellation Rejection  cancellation Rejection main alternative Rejection main alternative one would hope to retain dataone would hope to retain data Cancellation requirements Cancellation requirements clinical informationclinical information no new artifactsno new artifacts spike detectorsspike detectors Additive/multiplicative model Additive/multiplicative model Artifact reduction using linear filtering Artifact reduction using linear filtering

Artifact cancellation  Using linearly combined reference signals  Adaptive artfact cancellation using linearly combined reference signals  Using filtered reference signals

Linearly combined reference signals  Eye movements & blinks several referene signals several referene signals positioning positioning additive model additive model EOG linearly trasferred to EEG EOG linearly trasferred to EEG weightsweights

In detail  Uncorrelated  Mean square error  Minimization, differentation  Spatial correlation, cross correlation fixed over time fixed over time zero gradient zero gradient  Estimation blinks, eye-movements at onset blinks, eye-movements at onset

In detail 2  Number of reference signals  Only EOG cancelled  ECG  Rejection used a lot (in MEG) expect when lots of blinks (ssp) expect when lots of blinks (ssp)

Adaptive version  Time-varying changes  Tracking of slow changes  Adaptive algorithm LMS LMS weight(s) function of time weight(s) function of time optimal solution changes with timeoptimal solution changes with time method of steepest descent method of steepest descent negative error gradient vector negative error gradient vector

In detail  Parameter selection time time noise noise  Expectation instantaneous value instantaneous value zero setting zero setting performance estimation performance estimation fluctuation of weights fluctuation of weights

Filtered reference signals  EOG potentials exhibit frequency dependence in trasfer to EEG sensor through tissue in trasfer to EEG sensor through tissue blinks and eye movements blinks and eye movements  Improved cancellation with transfer function replacement spatial and temporal information spatial and temporal information v 0 estimation v 0 estimation FIR (lengths) FIR (lengths)

Details  Stationary processes Second order characterisrics Second order characterisrics Correlation information fixed Correlation information fixed

Details 2  No a priori information can be implemented, modified error can be implemented, modified error  Also adaptive version exists a priori impulse responses calculated at calibration a priori impulse responses calculated at calibration

Nonparametric spectral analysis  Richer characterization of background activity that with 1D histograms  EEG rhythms  Correlate signals with sines and cosines  When? Gaussian stationary signals Gaussian stationary signals Stationary estimatationStationary estimatation Normal spontaneous waking activity Normal spontaneous waking activity

Nonparametric 2  Fourier-based power spectrum analysis no modeling assumptions no modeling assumptions  Spectral parameters interpretation interpretation

Fourier-based power spectrum analysis  Power spectrum characterized by correlation function (stationary) If ergodic, approximate with time average estimator (negative lags) If ergodic, approximate with time average estimator (negative lags) combination called periodogram combination called periodogram equals squared magnitude of DFT equals squared magnitude of DFT

Fourier considerations  Periodogram 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 frequency bandsynchronized rhythm better described by power in frequency band variance periogoram variance periogoram does not approach zero with sample increasedoes not approach zero with sample increase consistency consistency

Periodogram  Windowing and averaging leakage & periodogram variance reduction leakage & periodogram variance reduction  Windows from rectangular to smaller sidelobes from rectangular to smaller sidelobes wider main lobe, spectral resolutionwider main lobe, spectral resolution  Variance reduction nonoverlapping segments, averaging nonoverlapping segments, averaging resolution decrease, trade-offresolution decrease, trade-off combinations, degree of overlapcombinations, degree of overlap

And then what...

Spectral parametrs  Resulting power spectrum often not readilty interpreted Condensed into compact set of parameters Condensed into compact set of parameters feature extraction feature extraction parameters describing prominent features of the spectrumparameters describing prominent features of the spectrum peaks, frequencies peaks, frequencies general usagegeneral usage

Spectral choices  Visual inspection format selection format selection assessing represantiveness assessing represantiveness  Scaling scope of the analysis scope of the analysis

Parameters  Power in frequency bands  Peak frequency  Spectral slope  Hjort descriptors  Spectral purity index

Power in frequency bands  Fixed/statistical bands alpha, beta, theta etc. alpha, beta, theta etc. from data from data  Ratio of, absolute power comparison, nonphysiological factors comparison, nonphysiological factors

Peak frequency  Frequency, amplitude, width  ad hoc methods for determining peaks  more than just maximum median, mean median, mean

Spectral slope  EEG activity made of 2 component rhythmic, unstructured rhythmic, unstructured  Based on decay of high frequency components one parameters approximation one parameters approximation least squares errorleast squares error  Quantifcation of EEG  Preconditioning of power estimate

Hjort descriptors  Spectral moments H 0 (activity) H 0 (activity) H 1 (mobility) H 1 (mobility) H 2 (complexity) H 2 (complexity)  Signal power, dominant frequency, bandwidth  Effectively in time domain  Clinically useful

Spectral purity index (SPI)  Heuristic  Reflects signal bandwidth (H 2 )  How well signal is described by a single frequency noise susceptibility noise susceptibility

Summary  Artifact cancellation reference signals reference signals linear combinations, filtering linear combinations, filtering adaptive version(s)adaptive version(s)  Spectral parameters nonparametric nonparametric no modellingno modelling parametric parametric interpretationinterpretation