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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

The spatial harmonic decomposition of the SEP data for one volunteer.(a) Averaged trials of the SEP data, 256 channels and the potential distribution for P14, N20, and N30 are shown. The view direction is top left. (b) Time-spatial-harmonic representation of the power of the SEP data using 60 BF with the lowest frequencies, starting with the low frequency at the bottom. (c) Contribution of selected BF to the MGFP of the SEP data. The MGFP is represented by the black line. The contribution of the BF is color-coded in the background, compare subfigure (e). (d) For each point of the time-spatial-harmonic representation, the square of the absolute value of the B-related inner product between the potential distribution and the BF is computed. (e) Selection of BF used for the data decomposition; note the different color scaling for each BF; the color code of the background is used in subfigure (c).
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pone.0121741.g005: The spatial harmonic decomposition of the SEP data for one volunteer.(a) Averaged trials of the SEP data, 256 channels and the potential distribution for P14, N20, and N30 are shown. The view direction is top left. (b) Time-spatial-harmonic representation of the power of the SEP data using 60 BF with the lowest frequencies, starting with the low frequency at the bottom. (c) Contribution of selected BF to the MGFP of the SEP data. The MGFP is represented by the black line. The contribution of the BF is color-coded in the background, compare subfigure (e). (d) For each point of the time-spatial-harmonic representation, the square of the absolute value of the B-related inner product between the potential distribution and the BF is computed. (e) Selection of BF used for the data decomposition; note the different color scaling for each BF; the color code of the background is used in subfigure (c).

Mentions: The SEP data of the eleven volunteers were decomposed by using the base functions for each of the three discretization approaches. The procedure of the spatial harmonic decomposition of the SEP data for one volunteer is illustrated in Fig 5. The SEP data consist of 256 EEG-channels, which are shown in Fig 5(a). The decomposition was performed by calculating the inner product of the multichannel data and the BF, see Fig 5(d). The power contribution of the spatial harmonic BF to the SEP data at each time step is shown in Fig 5(b), which shows the time versus spatial harmonic frequency representation of the decomposed 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)

The spatial harmonic decomposition of the SEP data for one volunteer.(a) Averaged trials of the SEP data, 256 channels and the potential distribution for P14, N20, and N30 are shown. The view direction is top left. (b) Time-spatial-harmonic representation of the power of the SEP data using 60 BF with the lowest frequencies, starting with the low frequency at the bottom. (c) Contribution of selected BF to the MGFP of the SEP data. The MGFP is represented by the black line. The contribution of the BF is color-coded in the background, compare subfigure (e). (d) For each point of the time-spatial-harmonic representation, the square of the absolute value of the B-related inner product between the potential distribution and the BF is computed. (e) Selection of BF used for the data decomposition; note the different color scaling for each BF; the color code of the background is used in subfigure (c).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0121741.g005: The spatial harmonic decomposition of the SEP data for one volunteer.(a) Averaged trials of the SEP data, 256 channels and the potential distribution for P14, N20, and N30 are shown. The view direction is top left. (b) Time-spatial-harmonic representation of the power of the SEP data using 60 BF with the lowest frequencies, starting with the low frequency at the bottom. (c) Contribution of selected BF to the MGFP of the SEP data. The MGFP is represented by the black line. The contribution of the BF is color-coded in the background, compare subfigure (e). (d) For each point of the time-spatial-harmonic representation, the square of the absolute value of the B-related inner product between the potential distribution and the BF is computed. (e) Selection of BF used for the data decomposition; note the different color scaling for each BF; the color code of the background is used in subfigure (c).
Mentions: The SEP data of the eleven volunteers were decomposed by using the base functions for each of the three discretization approaches. The procedure of the spatial harmonic decomposition of the SEP data for one volunteer is illustrated in Fig 5. The SEP data consist of 256 EEG-channels, which are shown in Fig 5(a). The decomposition was performed by calculating the inner product of the multichannel data and the BF, see Fig 5(d). The power contribution of the spatial harmonic BF to the SEP data at each time step is shown in Fig 5(b), which shows the time versus spatial harmonic frequency representation of the decomposed 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