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From wavelets to adaptive approximations: time-frequency parametrization of EEG.

Durka PJ - Biomed Eng Online (2003)

Bottom Line: 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.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.

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Affiliation: Laboratory of Medical Physics, Institute of Experimental Physics, Warsaw University, Warszawa, Poland. piotr@durka.info

ABSTRACT
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.

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Time-frequency energy density of a signal composed of two chirps presented in (a). In 3-dimensional plots on the left side energy is proportional to height, on flat pictures on the right – to the shades of gray. (b) presents results of a single decomposition over dictionary consisting of 500.000 atoms, and (c) – time-frequency representation averaged over 50 realizations of smaller dictionary (15.000 atoms)
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Figure 21: Time-frequency energy density of a signal composed of two chirps presented in (a). In 3-dimensional plots on the left side energy is proportional to height, on flat pictures on the right – to the shades of gray. (b) presents results of a single decomposition over dictionary consisting of 500.000 atoms, and (c) – time-frequency representation averaged over 50 realizations of smaller dictionary (15.000 atoms)

Mentions: Another interesting property of the stochastic time-frequency dictionaries, discussed in section 5.1, relates to the representation of structures of changing frequency. Such structures are absent in the dictionaries usually applied for the decomposition, and therefore are represented as a series od fixed-frequency Gabor functions (Figure 22 (f) and Figure 21 (b)).


From wavelets to adaptive approximations: time-frequency parametrization of EEG.

Durka PJ - Biomed Eng Online (2003)

Time-frequency energy density of a signal composed of two chirps presented in (a). In 3-dimensional plots on the left side energy is proportional to height, on flat pictures on the right – to the shades of gray. (b) presents results of a single decomposition over dictionary consisting of 500.000 atoms, and (c) – time-frequency representation averaged over 50 realizations of smaller dictionary (15.000 atoms)
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC149437&req=5

Figure 21: Time-frequency energy density of a signal composed of two chirps presented in (a). In 3-dimensional plots on the left side energy is proportional to height, on flat pictures on the right – to the shades of gray. (b) presents results of a single decomposition over dictionary consisting of 500.000 atoms, and (c) – time-frequency representation averaged over 50 realizations of smaller dictionary (15.000 atoms)
Mentions: Another interesting property of the stochastic time-frequency dictionaries, discussed in section 5.1, relates to the representation of structures of changing frequency. Such structures are absent in the dictionaries usually applied for the decomposition, and therefore are represented as a series od fixed-frequency Gabor functions (Figure 22 (f) and Figure 21 (b)).

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Laboratory of Medical Physics, Institute of Experimental Physics, Warsaw University, Warszawa, Poland. piotr@durka.info

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus