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.
The electroencephalogram (EEG), recorded from electrodes placed on the scalp, reflects the electrical activity of the brain. First registered from human scalp in 1929 [1], until today EEG remains an important tool in neuroscience and clinical neurophysiology. For a long time it was the only objective parameter providing information on brain’s function. Recently emerging dynamic imaging techniques like fMRI and PET offer a complementary information on brains functioning. Their drawbacks include significantly lower time resolution, high cost and invasiveness. Nevertheless, in spite of those drawbacks, they are often preferred for the straightforward interpretability. On the contrary, visual interpretation of EEG is a difficult, tedious and complicated task, requiring many years of experience. And even then it contains a significant subjective factor: Every experienced electroencephalographer has his or her personal approach to EEG interpretation. (…) there is an element of science and element of art in a good EEG interpretation; it is the latter that defies standardization. writes Prof. Ernst Niedermayer in the recent edition of a fundamental reference. In spite of this discouraging opinion, application of various signal processing methods in this field is still very popular. First introduction of Fourier analysis to EEG is dated 1932 . Since then spectral analysis has become a standard tool in this field. But until today, basically no other method gained a general acceptance – the few widely accepted and applied methods of EEG analysis still amount to :
1. visual analysis of raw EEG traces,
2. Fourier estimation of spectral power in selected frequency bands,
3. description of evoked potentials, averaged in the time domain.

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