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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

Example of noise suppression using spatial harmonic low pass filter.Left column unfiltered data, right column spatial harmonic low-pass filtered data; in the first row averaged SEP data without additional noise; in the following rows SEP data with additional Gaussian white noise with 3, 0, -3 dB signal to noise ratio.
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pone.0121741.g009: Example of noise suppression using spatial harmonic low pass filter.Left column unfiltered data, right column spatial harmonic low-pass filtered data; in the first row averaged SEP data without additional noise; in the following rows SEP data with additional Gaussian white noise with 3, 0, -3 dB signal to noise ratio.

Mentions: The capability of the new method for noise suppression is demonstrated by implementing a spatial low pass filter. For this purpose, we designed a filter with 25 low-frequency basis functions. Depending on the data of the volunteers, between 96.4 and 98.6% of the signal energy of the EEG data can be reconstructed with 25 low-frequency basis functions. In the simulation, performed to investigate the noise reduction, Gaussian white noise with different noise ratios was added to the averaged SEP data. Subsequently, the noisy data were low-pass filtered with Sphara. An example of the averaged SEP data, with additional Gaussian white noise and the results of the spatially harmonic low-pass filtering are shown in Fig 9. In a simulation with 100 000 repetitions, the ability of the spatial harmonic analysis for noise reduction could be shown. The improvement of the SNR by spatially harmonic low-pass filtering is in the median case between 4.31 dB and 9.74 dB, see Fig 10.


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)

Example of noise suppression using spatial harmonic low pass filter.Left column unfiltered data, right column spatial harmonic low-pass filtered data; in the first row averaged SEP data without additional noise; in the following rows SEP data with additional Gaussian white noise with 3, 0, -3 dB signal to noise ratio.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0121741.g009: Example of noise suppression using spatial harmonic low pass filter.Left column unfiltered data, right column spatial harmonic low-pass filtered data; in the first row averaged SEP data without additional noise; in the following rows SEP data with additional Gaussian white noise with 3, 0, -3 dB signal to noise ratio.
Mentions: The capability of the new method for noise suppression is demonstrated by implementing a spatial low pass filter. For this purpose, we designed a filter with 25 low-frequency basis functions. Depending on the data of the volunteers, between 96.4 and 98.6% of the signal energy of the EEG data can be reconstructed with 25 low-frequency basis functions. In the simulation, performed to investigate the noise reduction, Gaussian white noise with different noise ratios was added to the averaged SEP data. Subsequently, the noisy data were low-pass filtered with Sphara. An example of the averaged SEP data, with additional Gaussian white noise and the results of the spatially harmonic low-pass filtering are shown in Fig 9. In a simulation with 100 000 repetitions, the ability of the spatial harmonic analysis for noise reduction could be shown. The improvement of the SNR by spatially harmonic low-pass filtering is in the median case between 4.31 dB and 9.74 dB, see Fig 10.

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