From wavelets to adaptive approximations: time-frequency parametrization of EEG

This paper presents a summary of time-frequency analysis of the electrical activity of the brain (EEG). It covers in details two major steps: introduction of wavelets and adaptive approximations. Presented studies include time-frequency solutions to several standard research and clinical problems, encountered in analysis of evoked potentials, sleep EEG, epileptic activities, ERD/ERS and pharmaco-EEG. Based upon these results we conclude that the matching pursuit algorithm provides a unified parametrization of EEG, applicable in a variety of experimental and clinical setups. This conclusion is followed by a brief discussion of the current state of the mathematical and algorithmical aspects of adaptive time-frequency approximations of signals

Spindles in Svarog: framework and software for parametrization of EEG transients

We present a complete framework for time-frequency parametrization of EEG transients, based upon matching pursuit (MP) decomposition, applied to the detection of sleep spindles. Ranges of spindles duration (>0.5s) and frequency (11–16 Hz) are taken directly from their standard definitions. Minimal amplitude is computed from the distribution of the root mean square (RMS) amplitude of the signal within the frequency band of sleep spindles. Detection algorithm depends on the choice of just one free parameter, which is a percentile of this distribution. Performance of detection is assessed on the first cohort/second subset of the Montreal Archive of Sleep Studies (MASS-C1/SS2). Cross-validation performed on the 19 available overnight recordings returned the optimal percentile of the RMS distribution close to 97 in most cases, and the following overall performance measures: sensitivity 0.63±0.06, positive predictive value 0.47±0.08, and Matthews coefficient of correlation 0.51±0.04. These concordances are similar to the results achieved on this database by other automatic methods. Proposed detailed parametrization of sleep spindles within a universal framework, encompassing also other EEG transients, opens new possibilities of high resolution investigation of their relations and detailed characteristics.MP decomposition, selection of relevant structures, and simple creation of EEG profiles used previously for assessment of brain activity of patients in disorders of consciousness are implemented in a freely available software package Svarog (Signal Viewer, Analyzer and Recorder On GPL) with user-friendly, mouse-driven interface for review and analysis of EEG. Svarog can be downloaded from http://braintech.pl/svarog

Test of magnitude of nSNR response for pairs of frequencies.

<p>White pixel indicate a pair of stimulation frequencies (one from horizontal, and one from vertical axis) which do not show significant differences in mean nSNR response, black pixel indicates that the difference is significant. Color squares indicate contiguous frequency ranges which pairwise have equal mean responses.</p

Scheme of a single experimental trial.

<p>Resting period lasted 6(at 0 s.), the subject was instructed by a voice command to which of the fields he or she should attend. The signals from −6 to −2 s. of the resting epoch and signal from 0 to 4 s. of the stimulation epoch were selected for further analysis as No Visual Stimulation Epochs and Visual Stimulation Epochs, respectively.</p

Distribution of nSNR responses in selected frequency ranges.

<p>Each box-plot shows median (middle red line) together with its 95% confidence interval (notches). The lower and upper edge indicate 25 and 75 quantile, the whiskers show the span the data.</p

SSVEP frequency response curves.

<p>Columns correspond to the method of SSVEP evaluation: Left – spectral power, right – Signal to Noise Ratio. Rows 1–10 correspond to individual subjects, last row shows the response averaged across 10 subjects. Horizontal axis – stimulation frequency. Vertical axes have two scales. In the left column: left scale – normalized power , right scale – absolute mean power . In the right column: left scale – values of , right scale – values of . Error bars indicate the RMS error. Each plot presents two curves: the blue line shows values obtained for NVS, and the red one for VS condition. The gray regions in rows 1–10 mark the frequencies, where the given measure (column) gives significantly higher result for VS than NVS epochs for the a given subject (row) – results of within-subject level tests. The gray color on the plots in the last row means significant reactive frequencies for the population. Dotted vertical lines at 8 Hz and 13 Hz mark the range of the -band. Note: For S6 in left column the blue line exceeds the shown range to reach the value of .</p