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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 Universität 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

Number of coefficients that are required to achieve 90%, 95% and 99% of the total signal energy.(all samples in the time range from 50 ms before to 130 ms after stimulation). The left bars for each signal power threshold represent the results for TL, the middle bars for IE and the right bars for FEM, note the logarithmic scaling of the Y-axis.
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pone.0121741.g006: Number of coefficients that are required to achieve 90%, 95% and 99% of the total signal energy.(all samples in the time range from 50 ms before to 130 ms after stimulation). The left bars for each signal power threshold represent the results for TL, the middle bars for IE and the right bars for FEM, note the logarithmic scaling of the Y-axis.

Mentions: We investigated how many of the spatial-harmonic coefficients are required to achieve 90%, 95% and 99% of the signal energy of the samples in the time range from 50 ms before to 130 ms after stimulation. We compared BF, computed by the TL, IE and FEM approaches. In the first case, the individually tracked sensor positions of the volunteers were used to determine the BF using the IE and FEM approach. The BF of the TL approach can be determined without information of the sensor positions. The BF with the largest energy contribution are used for signal reconstruction. The results are shown in Fig 6. The available compression ratios in the best, in the median and in the worst case are listed in Table 1. The compression ratio is the quotient of the maximum number of available BF and the number of BF that are used to restore the signal at a given quality. A maximum of 256 basis functions are available to reconstruct the entire signal energy. The significance of the influence of the three discretization methods on the achieved compression ratio was analyzed using the Mann-Whitney U test. This test was chosen because not all examined data are normally distributed, tested by the Pearson χ2 test. None of the methods is significantly superior in reconstructing 90% of the signal energy. There is no significant difference between the TL and IE approach in the ability to present EEG data compactly. FEM provides significantly better results than TL and IE in the reconstruction of 95% and 99% of the signal energy, see Fig 6 and Table 2. The main contribution to the signal power of the SEP data is provided by the low frequency spatial-harmonic BF as exemplarily shown in Fig 5(b).


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)

Number of coefficients that are required to achieve 90%, 95% and 99% of the total signal energy.(all samples in the time range from 50 ms before to 130 ms after stimulation). The left bars for each signal power threshold represent the results for TL, the middle bars for IE and the right bars for FEM, note the logarithmic scaling of the Y-axis.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0121741.g006: Number of coefficients that are required to achieve 90%, 95% and 99% of the total signal energy.(all samples in the time range from 50 ms before to 130 ms after stimulation). The left bars for each signal power threshold represent the results for TL, the middle bars for IE and the right bars for FEM, note the logarithmic scaling of the Y-axis.
Mentions: We investigated how many of the spatial-harmonic coefficients are required to achieve 90%, 95% and 99% of the signal energy of the samples in the time range from 50 ms before to 130 ms after stimulation. We compared BF, computed by the TL, IE and FEM approaches. In the first case, the individually tracked sensor positions of the volunteers were used to determine the BF using the IE and FEM approach. The BF of the TL approach can be determined without information of the sensor positions. The BF with the largest energy contribution are used for signal reconstruction. The results are shown in Fig 6. The available compression ratios in the best, in the median and in the worst case are listed in Table 1. The compression ratio is the quotient of the maximum number of available BF and the number of BF that are used to restore the signal at a given quality. A maximum of 256 basis functions are available to reconstruct the entire signal energy. The significance of the influence of the three discretization methods on the achieved compression ratio was analyzed using the Mann-Whitney U test. This test was chosen because not all examined data are normally distributed, tested by the Pearson χ2 test. None of the methods is significantly superior in reconstructing 90% of the signal energy. There is no significant difference between the TL and IE approach in the ability to present EEG data compactly. FEM provides significantly better results than TL and IE in the reconstruction of 95% and 99% of the signal energy, see Fig 6 and Table 2. The main contribution to the signal power of the SEP data is provided by the low frequency spatial-harmonic BF as exemplarily shown in Fig 5(b).

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 Universität 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