STATISTICAL TIME-FREQUENCY DIFFERENTIATIONS OF ERP IN DYSLEXIA USING MATCHING PURSUIT ALGORITHM

The main purpose of this paper is to study energy differentiations of electroencephalogram (EEG) and event related potentials (ERP) of normal subjects and subjects with dyslexia. As ERP is considered to be nonstationary signal, traditional spectral analysis is not recommended. A most appropriate approach is time-frequency representation (TFR) which reveals temporal evolution of frequency components. In this study a non-orthogonal, iterative method for adaptive timefrequency approximation of signals called matching pursuit is used. This method decomposes the signal piece by piece using a dictionary of basis functions. At each step the best fitting analyzing function is adapted to an intrinsic structure of the signal, thus providing flexible signal representation. The major advantages of the matching pursuit are the good localization of transients, the robust universal estimate of the time-frequency energy density which is resistant to the existence of noise and the fact that the dictionary set of waveforms is not limited to a single basis. Time frequency statistics reveal statistical differences on energy distribution of specific time intervals and frequency components over time-frequency plane. Possible non-normal distributions of the energy values are taken into account and a normalization transform is used in order to be able to use robust parametric tests. According to this analysis, dyslexics appear to have statistically reduced energy compared to controls for frequency regions 5-20Hz and for time around the ERP component N100. Introduction In the present paper, the matching pursuit algorithm, which was first proposed by Mallat and Zhang [1] is applied in order to estimate the energy of EEG signals in time-frequency plane. The use of matching pursuit algorithm leads to a decomposition of each EEG signal into a linear expansion of Gabor atoms. The timefrequency estimation of EEG signal energy is the result of pseudo Wigner-Ville distribution of Hilbert transform of these Gabor atoms. In previous works have been used some other methods in estimation of EEG signal energy in timefrequency plane like spectrogram [2], scalogram [3], bandpass filtering in overlapping bands [4]. The approximation of a signal using nonorthogonal functions is a “nonpolynomial” problem (computational complexity grows exponentially with the dimension of signal). The matching pursuit algorithm is a sub-optimal solution but as the heuristic give relatively small error this can’t be considered as drawback. The major advantages of matching pursuit in contrary to the other time-frequency methods is that provides an optimal non-orthogonal selection of basis atoms and full parametrization of these atoms. The above features of matching pursuit is very important in time-frequency analysis of non-stationary signal like EEG/ERP, whose temporal changes in energy are significant as they are associated with functional brain activation. No other methods possess these properties. For example, the Fourier analysis which used in spectrogram localization in time and frequency depends on epoch length (the STFT spectrogram divides the analyzed signal into overlapping epochs). Continuous wavelet transform or Cohen’s class transforms do not provide parametric description. Moreover Cohen’s class transforms are biased by cross-terms. Discrete wavelet transforms, which used in scalogram give parametric descriptions, but their time-frequency resolution is severely limited as it has high temporal resolution and low frequency resolution at high frequencies, and low temporal resolution and high frequency resolution at low frequencies [5]. According to earlier works the matching pursuit algorithm provides a unified parametrization of EEG, applicable in a variety of several standard research and clinical problems, encountered in analysis of evoked potentials [6], automatic detection and analysis of sleep spindles in overnight EEG recordings [7], ERD/ERS [6][8], pharmaco-EEG [9] and epileptic seizures [10][11].