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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.

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.

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Related in: MedlinePlus

Distinction between a spectral power integral from f1 to f2, and power actually carried by structures of frequencies centered between f1 and f2. Plot a) presents spectral power (versus frequency) of hypothetical structures with frequency centers lying inside (dotted) and outside (dashed line) the f1-f2 interval. Due to the uncertainty principle, their spectral contents overlap. Solid line presents their sum, i.e. total spectral power, as estimated e.g. by Fourier transform. In b) the actual power carried by structure of frequency originating between f1 and f2, as estimated in the proposed approach, is shaded. Plot c) highlights the power obtained from a spectral integral from f1 to f2. Finally in d) additional background (dotted-dashed line) is added. We observe that neighboring structures from outside the interval of interest may contribute significantly to the power estimated within the interval, and can even shift the actual position of the spectral peak related to the relevant structure (dotted line), while some of the power carried by the structure inside the interval of interest falls outside and does not contribute to the spectral integral
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Figure 20: Distinction between a spectral power integral from f1 to f2, and power actually carried by structures of frequencies centered between f1 and f2. Plot a) presents spectral power (versus frequency) of hypothetical structures with frequency centers lying inside (dotted) and outside (dashed line) the f1-f2 interval. Due to the uncertainty principle, their spectral contents overlap. Solid line presents their sum, i.e. total spectral power, as estimated e.g. by Fourier transform. In b) the actual power carried by structure of frequency originating between f1 and f2, as estimated in the proposed approach, is shaded. Plot c) highlights the power obtained from a spectral integral from f1 to f2. Finally in d) additional background (dotted-dashed line) is added. We observe that neighboring structures from outside the interval of interest may contribute significantly to the power estimated within the interval, and can even shift the actual position of the spectral peak related to the relevant structure (dotted line), while some of the power carried by the structure inside the interval of interest falls outside and does not contribute to the spectral integral

Mentions: Figure 20 partially explains the increased sensitivity of the proposed approach as compared to the classical paradigm of band-limited spectral power integrals.


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

Durka PJ - Biomed Eng Online (2003)

Distinction between a spectral power integral from f1 to f2, and power actually carried by structures of frequencies centered between f1 and f2. Plot a) presents spectral power (versus frequency) of hypothetical structures with frequency centers lying inside (dotted) and outside (dashed line) the f1-f2 interval. Due to the uncertainty principle, their spectral contents overlap. Solid line presents their sum, i.e. total spectral power, as estimated e.g. by Fourier transform. In b) the actual power carried by structure of frequency originating between f1 and f2, as estimated in the proposed approach, is shaded. Plot c) highlights the power obtained from a spectral integral from f1 to f2. Finally in d) additional background (dotted-dashed line) is added. We observe that neighboring structures from outside the interval of interest may contribute significantly to the power estimated within the interval, and can even shift the actual position of the spectral peak related to the relevant structure (dotted line), while some of the power carried by the structure inside the interval of interest falls outside and does not contribute to the spectral integral
© Copyright Policy
Related In: Results  -  Collection

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

Figure 20: Distinction between a spectral power integral from f1 to f2, and power actually carried by structures of frequencies centered between f1 and f2. Plot a) presents spectral power (versus frequency) of hypothetical structures with frequency centers lying inside (dotted) and outside (dashed line) the f1-f2 interval. Due to the uncertainty principle, their spectral contents overlap. Solid line presents their sum, i.e. total spectral power, as estimated e.g. by Fourier transform. In b) the actual power carried by structure of frequency originating between f1 and f2, as estimated in the proposed approach, is shaded. Plot c) highlights the power obtained from a spectral integral from f1 to f2. Finally in d) additional background (dotted-dashed line) is added. We observe that neighboring structures from outside the interval of interest may contribute significantly to the power estimated within the interval, and can even shift the actual position of the spectral peak related to the relevant structure (dotted line), while some of the power carried by the structure inside the interval of interest falls outside and does not contribute to the spectral integral
Mentions: Figure 20 partially explains the increased sensitivity of the proposed approach as compared to the classical paradigm of band-limited spectral power integrals.

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