Aufrichtigl, Richard

Jennum, Poul

Pedersen, Simon Boel

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Adaptive Segmentation Of EEG SignalsAufrichtigl, Richard; Pedersen, Simon Boel; Jennum, PoulPublished in:Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology SocietyPublication date:1991Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Aufrichtigl, R., Pedersen, S. B., & Jennum, P. (1991). Adaptive Segmentation Of EEG Signals. In Proceedings ofthe Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Vol. Volume 13,pp. 453-454). IEEE.Processing of Biological Signals 30.9-4 ADAPTIVE SEGMENTATION OF EEG SIGNALS Richard Aufrichtig1*2, Simon Boel Pedexn' and Poul Jennurd 'Electronics Institute, The Technical University of Denmark, DK 2800. Denmark 'Dept. of Biomedical Engineering. Case Westem Reserve University, Cleveland, OH 44106, USA 3Dept. of Neurology, University Hospital of Copenhagen, Hvidovre Hospital, DK 2650, Denmark ABSTRACT This paper decribes the application of xlaptive segmentation techniques to EEG-signals. A number of methods to detect abrupt changes in the signal are discussed. assuming that it can be modelled as realizations of quasi-stationary autoregressive (AR) pmxsses. Earlier plblished methods are revised to obtain symmetrical de&tion. so that a comparable segmenta- tion pedormance is achieved independent of the change in power across a segment boundary. Simulation studies are used to rank the methods. INTRODUCTION EEG recordings vary due to changes in the physiological or psychologi- cal state of the subject. The implication is that the statistical characteris- tics of the EEG vary with time.. and the signal is therefm considered to be non-stationary. This pcwes a significant problem in EEG analysis, since the basic assumption in the use of classical analysis methods (spectral-, period- and correlation-analysis) is that the signal is stationary. The problem of detecting abrupt changes, and segmenting the signal into quasi-stationary parts has been a continuing subject of research for many years [l ,  2. 4. 51. This study outlines the method of adaptive segmentation. It assesses some of the limitations of previous methods and presents modifications of them. The performance of the described algorithms are compared and evaluated in a simulation study. THEORY In order to perform a segmentation of the EEG signal we assume that a homogenous part of the signal can be modelled as a realization of an autoregressive (AR) process: P x(n) = 4 x(n - k) + e h )  (1) k = l  where p is the model order, a are the AR-parameters and e(n) is a zro  mean white mise se~uence with variance U:. The parametric AR-model has often been applied to EEG signals with orders varying from 5 to 15 depending on the length of the signal and the model application [l,  21. The advantage of using an AR-mode1 is that the statistical properties are solely described by the. set of AR-parameters. which are constant within a stationary segmenL It is therefore sufficient to detect achange in h s e  parameters to detect a segmentboundary. The principle in adaptive fillering, as Originally proposed by [41 is as follows. Features from an initial reference window are extracted and continuously compared with those of a moving window of EEG signal. A segment boundary is detected when the featms of the reference window differ s ign i f i l ly  from lhose of the moving window. A new reference window is then specified following the boundary and the procedure is repeated. Applying AR-modelling, the comparison between the reference and the moving windows can be done in the following ways: I. An AR-model is estimated for the reference window and the signal in the moving window is filtered with the. corresponding inverse filter. The basic assumption is that the output of the filmtion will be a zero mean white noise residual signal. The. comparison is therefore reduced to a test of how far the residual signal is from the white noise hypothesis. This method has been extensively used [l, 3.4.51 and a typical test statistic of how far the residual signal is from the white noise. hypothesis has been based upon the cumulative sum of the residuals: (2) w k N ,  is the number of samples in the moving window, e&) is the residual signal and U: is the estimated noise variance of the reference window. Under the hypothesis that the signal is Gaussian and that no change occurs, this test statistic is asymptotically Gaussian distributed as N(0, 1). At first glance, the test seems to be effective, but it has been shown that it posses some serious drawbacks [3]. A problem occus when the signal undergoes a change with a decrease in energy, i.e. when < U',. In this case the drift of the test statistic can be positive as well as negative. Such a situation occurs regularly in EEG signals, e.g. in sleep recordings with transitions between sleep stages. 11. A simple solution to the asymmetry of the test statistic in Eq. (2) can be achieved by performing a dual inverse filtering, followed by a calculation of a cumulative test statistic. More specifically, an AR-model is estimated for the reference window, followed by an inverse filtering of the moving window, and a calculation of the slaristic Z,. Now a new AR- model is estimated for the moving window, followed by an inverse filtering and calculation of test statistic for the reference window. A final statistic can now be calculated as Ihe sum of the two intermediate values: This two step calculation insures a symmetrical detection of a change between two models, independent of whether there is an increase or decrease in energy across a segmentboundary. The use of Eq (3) is not without problems. Since it is now also necessary to estimate an AR-model for the moving window, the number of samples in this must be increased. The result is a smaller accuracy in the exact segment boundary. Furthermore the cumulated statistic does not follow a simple distribution due to the dependency between the two inverse filtrations. This means, that the segment boundary must be determined, when Z is larger than an empirically calculated threshold value. In practice this does not pose a problem, since the EEG signal is rarely Gaussian disuibuted. Empirical thresholding is therefore generally also required when Eq. (2) is used. IIl. A different approach from the inverse filtering, which can be used to compare the AR-parameters of the reference and moving windows has been described in [6]. In the derivation of the method, the asymptotic Gaussian Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 13. No. 1, 1991 0453 CH3068-419 1 10000-0453 SO 1 .OD 0 199 1 IEEE Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on July 06,2010 at 07:01:35 UTC from IEEE Xplore.  Restrictions apply. distribution of the AR-parameters is used to achieve a test statiaic far the diffemlcebetween the twosefsof AR-pmmaexs: where N are the number of samples, a = [ 81.82, ... ; b l T a r e t h e ~  ARcoefficients, d is the estimated noise variance and Rp is the p x p autocorrelation matrix of the signal. The subscripis r and m refer to the reference and moving windows respectively. It is shown that ZI  is IV. Itcanbeseendirectly from Eq. ( 4 ) t h a t h ~ o n l y  Rr is used, this test also possesses some asymmetry, and to compensate for this, the following statistic is consrmcted: asympto(ically X*l) distributed. z12 =z1+ z, ( 5 )  where Z1 is identical to the expression in Eq. (4) while 22 has the subscripts r and m r e v d ,  when compared to Eq. (4). Compared to Z1 in Eq. (4) there is only a very little increase in the computational work when Z12 is used. since both autocarrelaton matrices already have been calculated during the parameter estimation. As in the case of the dual inverse filtration test, the test statistic, Z12, must be compared to an empirical threshold value. EVALUATION OF METHODS Methods I, II, III and IV described in the previous section has been applied to simulated as well as real EEGs [l]. An example of a simulated test signal is shown in Figure 1. signal 1 signal2 o /  ... ... { I I I 4800 49W Moo 5100 5200 No. of Samples Flgure 1. Part of test sipal at boundary between simulated rraliutions of two AR(14)-models. The test signal consist of 2 x 5000 samples, from two simulated realizations of AR(14)-models. The fm part (Signal 1) is a simulated EEG signal from 14 AR-parameters estimated from a true EEG signal. For the simulation of the second part (Signal 2). one of the reflection coefficients from the model of Signal 1 was changed (there is a direct relationship between the AR-parameters and the reflection coefficients of an AR-model. The advantage of changing a reflection coefficient, to obtain an new model, is that stability of the system is insured. as long as the absolute values of the reflection coefficients m less than one [I]). The variance of the noise was a%1 = 0.35 for Signal 1. while it was changed to a%z = 0.48 for Signal 2. Since a transition from Signal 1 to Signal 2 is an increase in & one would therefore expect all 4 methods to detect the change, while at least method I would fa& if the two signal were reversed. This is confmed by the result in Figure 2. Notice that the reference window is kept at the initial position, even afm the transition, to follow the values of the test statistics. A significant improvement is achieved when either meihod I1 or IV is used. and it is in both cases possible to detect the boundary (absolute symmetry is not achieved, since the reference windows are different in the two cases). No significant difference has been observed between method I1 and IV, and method IV should therefore be recommended, since it is p l y  parametrical and does not require inverse filtering. REFERENCES R. Aufrichtig. "Adaptive segmentation of EEG signals", Master Thesis, Institute of Electronics, The Technical University of Denmark, (in Danish). De=& 1990. J.S. Barlow, "Methods of Analysis of Nonstationary EEGs, with Emphasis on Segmentation Techniques: A Comparative Review", I. Clin. Neurophysiol., Vol. 2, pp. 267-303 1985. M. Basseville and A. Benvenista, "Sequential Segmentation of Non- stationary Digital Signal Using Spectral Analysis", Information Sciences, Vol. 29. pp. 57-73: 1983. G. Bodenstein and H.M. Praetorius , "Feature Extraction from the Electroencephalogram by Adaptive Segmentation", Pmc. IEEE, Vol. 65, pp. 642-652 1977. A.C. Sanderson and J. Segen, " Hierarchical Modelling of EEG Signals", IEEE Trans. Pat. Anal. Mach. Intel., Vol. PAMI-2, pp. 405415 1980. P. Stoica, "Performance Evaluation of some Methods for Off-Line Detection of Changes in Autoregressive Signals", Signal Process., Vol. 19, pp. 301-310 1990. Address for correspondence: Department of Biomedical Engineering WicLendenBuilding Case Westem Reserve University Cleveland, OH 44106 Tel: 216 - 368 8812 Richard AufrichIig Figure 2. Values of test statistics after segmentation in test signal. In the right column (A, B. C and D), the reference window was the fmt 300 samples of Signal 1. while the moving window (also 300 samples) was sliding along signal 1 followed by signal 2. In the left column (E, F. G and H) the signals were reversed. Now the reference window was the first 300 samples of Signal 2, while the moving window was sliding along the rest o f  Signal 2 followed by Signal I .  Fig. A and E m e M  1 Fig. B and F method I1 Fig. C and G: method III Fig. D and H method IV M O . . . .  zoo- D 0 1000 2000 3000 100 5000 60oo 7000 8ooo 9ooo lwoo 0 1000 2000 Moo 4000 Moo fxxm 7000 8Ooo 9OoO lwoo 0454 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 13, No. 1, 1991 CH3068-4/91/0000-0454 $01.00 0 1991 IEEE Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on July 06,2010 at 07:01:35 UTC from IEEE Xplore.  Restrictions apply. 

Adaptive Segmentation Of EEG Signals

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Adaptive Segmentation Of EEG Signals

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