Event-related changes of energy in different EEG frequency bands are an important indicator of the underlying brain processes. Sensory processing and motor behavior are connected with the localized decrease of power in certain frequency bands, particularly in the alpha band. This phenomenon was called event related desynchronisation (ERD). The following increase in power after the event was named event related synchronisation (ERS). These effects, particularly in the context of movement planning, were extensively studied by Pfurtscheller [1], who also defined the ERD/ERS as the change in power in particular frequency band relative to the pre-movement epoch. The investigation of the ERD/ERS phenomena, apart from the clinical and scientific merits, has also technological implications: it opens the possibility of a brain-computer interface design [2]. Therefore, the quantification of the EEG reactivity to the externally or internally paced events and the assessment of the significance of changes have broad implications.
The classical method of quantification of event-related desynchronization and synchronization (ERD/ERS) [1] consists of time averaging the squared values of the samples of single trials, band-pass filtered in a priori selected bands. In 1993 S. Makeig [3] presented event-related spectral perturbation, that is time-varying spectra, estimating the time-frequency dynamics of underlying processes. Such an exploratory approach, free of a priori assumptions on fixed frequency bands, is widely used in last years, c.f. [4][5][6][7] to quote only few related works.
Different methods were used for estimating the time-frequency density of signals energy--apart from the short-time Fourier transform (STFT), e.g. smoothed Wigner-Ville distributions [5][6] and continuous wavelet transforms [8][4]. All these functions estimate the same quantity--time-frequency energy density of the signal. However, results may vary significantly not only depending on the chosen method, but also on its parameters (chosen wavelet, smothing of Wigner-Ville distribution, etc.). This produces an additional--apart from the unavoidable inter-subject variability--noise in the published results and makes difficult comparison of different findings, also reducing the value of neurophysiological conclusions drawn from these works. On the other hand, it is hard to judge a priori which of the estimators is ``better'' when analyzing signals of unknown content, in the absence of well defined criteria.
In 2001 the application of adaptive approximations, implemented the matching pursuit (MP) algorithm, was proposed for ERS/ERD estimation in the time-frequency space [9]. It proved to be a robust estimator, offering the best time-frequency resolution and high sensitivity in the investigation of the microstructure of ERD/ERS. It revealed the detailed structure of the gamma activity and the dependence between beta and gamma components [9]. In [10] the spatio-temporal behavior of different components of mu and beta rhythms was studied--using MP estimates--in the context of their functional role in movement preparation. Finally, this paper provides a framework for comparing the performance of different time-frequency estimators in the task of detecting event-related changes of energy (accompanying software implements MP and STFT, extensions of the system are being developped).
Apart from the discrepancies in the approach to the very issue of estimation of the time-frequency energy density of signals, the question of significance of changes, indicated by these estimators, remains an open issue. It seems to be a crucial point, essential to any procedure which is supposed to bring clinical or research conclusions.
Previous approaches include e.g. [3], [4] and [5], where selected time-frequency regions were compared between different experimental conditions. But the most common need is to evaluate the significance of a given ``burst" (time-frequency region of visible change) in relation to a reference period. When we see e.g. ``some increase'' in a given epoch and frequency, we must ask, before drawing any conclusions, whether this is a statistically significant effect or just a fluctuation. In spite of this, up to now only few works addressed this issue.
E.g. in [6] the significance of an occurence of a burst of activity was estimated and
displayed for a single frequency band; the issue of multiplicity in case of several
frequency bands was mentioned, but not investigated. In [7] resampling tests
were performed for each frequency band separately, and their results were displayed
together on a common time-frequency plane. A direct interpretation of such a map of
``significant changes'' may lead to neglecting the influence of multiple
comparisons [11]. For testing the hypothesis of no change in
one frequency band, we assume a significance level 
, corresponding to the
probability of type I error (rejecting a true hypothesis). This is valid for a single
hypothesis, which includes a priori choice of the frequency band of interest. But in the
exploratory analysis, when statistically significant results are displayed for an array
of frequencies, the probability of type I error for the whole family of hypotheses can
increase dramatically above the significance level assumed for a single frequency band.
A region picked from such a map should not be interpreted as significant at the claimed
significance level .
In this paper we present and discuss a complete framework for estimating significant changes in the average time-frequency density of energy of event-related signals. The method is presented in the context of ERD and ERS of the brain electrical activity. It consists of the following steps:
The following section gives a general discussion of applied methods, and section III presents their application.