Artifact cancellation and nonparametric spectral analysis Outline Artifact

Artifact cancellation and nonparametric spectral analysis

Outline Ø Artifact processing Ø Artifact cancellation Ø Nonparametric spectral analysis

Introduction Ø Artifact processing l l Rejection cancellation Rejection main alternative • one would hope to retain data l Cancellation requirements • clinical information • no new artifacts • spike detectors l l Additive/multiplicative model Artifact reduction using linear filtering

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

Linearly combined reference signals Ø Eye movements & blinks l l several referene signals positioning additive model EOG linearly trasferred to EEG • weights

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

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

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

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

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

Details Ø Stationary processes l l Second order characterisrics Correlation information fixed

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

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

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

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

Fourier considerations Ø Periodogram biased l l l window dependent (convolution) smearing (main lobe) leakage (side lobes) • synchronized rhythm better described by power in frequency band l variance periogoram • does not approach zero with sample increase l consistency

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

And then what. . .

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

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

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

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

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

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

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

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

Summary Ø Artifact cancellation l l reference signals linear combinations, filtering • adaptive version(s) Ø Spectral parameters l nonparametric • no modelling l parametric • interpretation