Matching Pursuit Parametrization of Sleep Spindles

Sleep spindles are transients important in evaluation of sleep EEG. Matching Pursuit (MP) is a recently introduced adaptive time-frequency method of signal analysis. Iterative algorithm fits to the local signal structures waveforms from a large an redundant set. 21 channels of an overnight EEG recording were subjected to the MP decomposition. Structures corresponding to sleep spindles were chosen from waveforms fitted to the signal. In this way sleep spindles were described in terms of natural parameters, i.e. position in time and frequency, width in time, amplitude and phase. Comparison of this automatic detection with visual analysis showed concordance decreasing with threshold amplitude. Characteristics of spindles occurrence in time, frequency and space were evaluated. Results confirmed several of the hypotheses reported in literature. INTRODUCTION Most of the methods of EEG analysis applied up to now such as Fourier Transform or autoregressive models provided general frequency characteristics of the time series but did poorly in describing transients and non-stationary signals. A progress in respect of evaluation of this kind of signals was introduced by wavelet transform (WT), but the method has also some serious limitations related to the pre-defined orthonormal basis. WT is well suited to the analysis of timelocked phenomena as evoked potentials, but does poorly for transients occurring more or less randomly in the signal [1]. A general solution for the above limitations can be achieved by using a redundant set of waveforms instead of orthonormal basis. However, the problem of choosing the waveforms that would best explain the signal’s variance is NP-hard [2]. Matching Pursuit, introduced by Mallat and Zhang in 1993 [3], provides a sub-optimal solution. Detection of sleep spindles in EEG was traditionally performed by visual analysis, although several automatic methods were tuned to reproduce visual detection. However, most of them inherited the main limitation of visual analysis: ’visibility’ of a structure dependent on a local S/N ratio. METHOD A large and redundant family of waveforms, called timefrequency atoms, is generated by scaling, translating and modulating a window function g(t): ( 1 ) gs,ξ ,u(t) 1 s g( t u s ) e iξt s>0 is scale, ξ frequency modulation and u translation. The windowed Fourier transform and wavelet transform can be considered as particular cases of MP corresponding to restrictions concerning the choice of parameters. In each step of an iterative procedure an atom giving the largest product with the residuum left after previous iterations is chosen. In this way a representation is adapted to the local signal structures. The energy is conserved. MP procedure was applied to 21 channels (10/20 system) of second night EEG of 8 healthy subjects (sampling frequency 102.4 Hz). Gabor functions were used as basic waveforms, i.e. the window function g in eq. (1) was Gauss. Such a choice provides the best time-frequency resolution and corresponds well to the shape of sleep spindles. EEG segments od 20 sec length were decomposed. Sleep spindles were chosen from the fitted atoms based upon their time-frequency features reported in literature: frequency 11-15 Hz and time span 0.6 2.4 sec. The problem of spindle’s amplitude threshold is still under investigation; for the plot presented here it was set at 20 μV. RESULTS Concordance of sleep spindles detection based upon MP parameters with human judgment revealed that the number of false positives increased for lower threshold amplitudes. This is due to the fact that the MP representation is adapted to the local signal structures, regardless of their ’visibility’, which depends on the on-going EEG. Some structures classified by expert as one spindle were identified by MP as a superposition of spindles with different frequencies. In the framework of MP, discrimination of such structures is straightforward. This problem was previously assessed by Hao et al [5], who applied complex demodulation to visually scored sleep spindles in order to resolve spindles partially overlapping in time domain. For 21 decomposed EEG channels detected spindles were described in terms of position in time and frequency, amplitude, and time span. Plots of spindle’s amplitudes and density vs time confirmed their reciprocal relation to the slow wave activity and absence of spindles of amplitude above 20 μV in the REM sleep episodes. Figure 1 presents each of detected spindles marked in the frequency-amplitude coordinates for 8 out of 21 analyzed derivations. Frequency distribution of spindles in recorded EEG channels reveals the predominance of low-frequency spindles in frontal and high-frequency spindles in posterior derivations as postulated by [4]. The abundance of spindles in temporal and occipital derivations was smaller than in the other localizations. Figure 1 Sleep spindles plotted in the frequencyamplitude coordinates for 8 of the 21 derivations. x frequency, y amplitude for each of the detected spindles. Frontal derivations in the upper part. DISCUSSION AND CONCLUSIONS Adaptivity of the MP representation allows precise detection of transients even at relatively low S/N ratio, where the ’visibility’ of the structures is poor. Most of the methods of automatic sleep spindles detection, applied up to now, were aimed at highest possible concordance with visual analysis. MP allows a step beyond the limitations of visual analysis and automatic methods aimed at imitating the human detection. Several of the spatial and temporal characteristics of spindles occurrence, postulated in literature and previously assessed by means of various techniques, were confirmed based upon the results of MP decomposition and automatic choice of structures corresponding to sleep spindles and slow wave activity. MP overcomes limitations inherent to wavelet transform, related to the fixed orthonormal basis. If offers a unique possibility of non-stationary signals representation in timefrequency-energy coordinates and of identification and parametrization of transients. We have demonstrated the advantages of the method on the example of sleep spindles. However, the application of MP-based techniques is by no means limited to this type of structures. Work aimed at complete description of sleep EEG based upon MP decomposition is in progress. ACKNOWLEDGEMENTSThis work was supported by KBN grant 8T11E 01209.We thank prof. W. Szelenberger from Warsaw Medical Schoolfor providing the data and consultations. REFERENCES[1] Blinowska K.J., Durka P.J. "The Application of WaveletTransform and Matching Pursuit to the Time-VaryingEEG Signals", Intelligent Engineering Systems throughArtificial Neural Networks, Vol.4 Ed. Dagli, Fernandez,Gosh, 1994 pp. 535-540[2] Davis G. "Adaptive Nonlinear Approximations" -a dissertation: Courant Institute of Mathematical Sciences,New York University, September 1994ftp://cs.nyu.edu/pub/wave/report/DissertationGDavis.ps.Z[3] Mallat S.G., Zhang Z. "Matching Pursuit with Time-Frequency Dictionaries." IEEE Trans. Sign. Process.,Vol. 41 pp. 3397-3415, 1993.[4] Jobert M., Poiseau E., Jähning P., Schultz H., Kubicki S."Topographical Analysis of Sleep Spindle activity"Neurobiology, Vol. 26, pp. 210-217, 1992.[5] Hao Y.L., Ueda Y., Ishii N. 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