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SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

Graichen U, Eichardt R, Fiedler P, Strohmeier D, Zanow F, Haueisen J - PLoS ONE (2015)

Bottom Line: Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction.Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary.We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universit├Ąt Ilmenau, Ilmenau, Germany.

ABSTRACT
Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

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Related in: MedlinePlus

FEM vs. PCA vs. ICA.The comparison of the effect on the compact representation of the investigated EEG data.
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pone.0121741.g008: FEM vs. PCA vs. ICA.The comparison of the effect on the compact representation of the investigated EEG data.

Mentions: We compared the FEM approach with PCA and ICA regarding the ability of a compact representation of EEG data in a spatial aspect. In PCA, the PC are sorted in decreasing order by there variances, which represents their energy contribution to the investigated data. In the Infomax-based ICA, the independent components (IC) are sorted in descending order of mean projected variance. The maximum number of IC that are to be calculated is determined by the rank of the covariance matrix of the analyzed data. The number of BF, PC and IC to achieve 90%, 95% and 99% of the signal energy of the investigated EEG data are evaluated. The results are shown in Fig 8. PCA comprises clearly the best performance on the compact representation of the EEG data. The second best compression ratio achieved the Sphara approach. ICA revealed the worst performance for the investigated EEG data.


SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

Graichen U, Eichardt R, Fiedler P, Strohmeier D, Zanow F, Haueisen J - PLoS ONE (2015)

FEM vs. PCA vs. ICA.The comparison of the effect on the compact representation of the investigated EEG data.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4401437&req=5

pone.0121741.g008: FEM vs. PCA vs. ICA.The comparison of the effect on the compact representation of the investigated EEG data.
Mentions: We compared the FEM approach with PCA and ICA regarding the ability of a compact representation of EEG data in a spatial aspect. In PCA, the PC are sorted in decreasing order by there variances, which represents their energy contribution to the investigated data. In the Infomax-based ICA, the independent components (IC) are sorted in descending order of mean projected variance. The maximum number of IC that are to be calculated is determined by the rank of the covariance matrix of the analyzed data. The number of BF, PC and IC to achieve 90%, 95% and 99% of the signal energy of the investigated EEG data are evaluated. The results are shown in Fig 8. PCA comprises clearly the best performance on the compact representation of the EEG data. The second best compression ratio achieved the Sphara approach. ICA revealed the worst performance for the investigated EEG data.

Bottom Line: Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction.Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary.We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biomedical Engineering and Informatics, Faculty of Computer Science and Automation, Technische Universit├Ąt Ilmenau, Ilmenau, Germany.

ABSTRACT
Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

Show MeSH
Related in: MedlinePlus