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Noise-assisted instantaneous coherence analysis of brain connectivity.

Hu M, Liang H - Comput Intell Neurosci (2012)

Bottom Line: Characterizing brain connectivity between neural signals is key to understanding brain function.In our method, fully data-driven MEMD, together with Hilbert transform, is first employed to provide time-frequency power spectra for neural data.Furthermore, a statistical randomization procedure is designed to cancel out the effect of the added noise.

View Article: PubMed Central - PubMed

Affiliation: School of Biomedical Engineering, Science & Health Systems, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA.

ABSTRACT
Characterizing brain connectivity between neural signals is key to understanding brain function. Current measures such as coherence heavily rely on Fourier or wavelet transform, which inevitably assume the signal stationarity and place severe limits on its time-frequency resolution. Here we addressed these issues by introducing a noise-assisted instantaneous coherence (NAIC) measure based on multivariate mode empirical decomposition (MEMD) coupled with Hilbert transform to achieve high-resolution time frequency representation of neural coherence. In our method, fully data-driven MEMD, together with Hilbert transform, is first employed to provide time-frequency power spectra for neural data. Such power spectra are typically sparse and of high resolution, that is, there usually exist many zero values, which result in numerical problems for directly computing coherence. Hence, we propose to add random noise onto the spectra, making coherence calculation feasible. Furthermore, a statistical randomization procedure is designed to cancel out the effect of the added noise. Computer simulations are first performed to verify the effectiveness of NAIC. Local field potentials collected from visual cortex of macaque monkey while performing a generalized flash suppression task are then used to demonstrate the usefulness of our NAIC method to provide highresolution time-frequency coherence measure for connectivity analysis of neural data.

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Decomposition of a synthetic trivariate nonstationary signal [X Y Z] via MEMD. The decomposed three IMFs C1–C3 correctly recover the designed components in the data (Figure 2).
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fig3: Decomposition of a synthetic trivariate nonstationary signal [X Y Z] via MEMD. The decomposed three IMFs C1–C3 correctly recover the designed components in the data (Figure 2).

Mentions: The MEMD was first performed to decompose the synthetic nonstationary data. Figure 3 showed that the raw data were decomposed into three IMFs, which correctly recovered the designed components in the data (Figure 2), and the common modes within the data were aligned in the IMFs with the same index. By virtue of Hilbert transform, each time series was represented by a time-frequency analytic matrix. A random noise complex matrix with noise variance of 10−4 was then superposed to the analytic matrix of clean data so as to facilitate the calculation of coherence between channels. Figure 4 showed time-frequency coherence based on the mixed data. From this figure, we can see that the obtained time-frequency coherence spectra reflect the designed coupling between channels. We notice, however, that the added noise induces some artifacts, shown as the bright spots scattered in the spectra. We subsequently performed the statistical randomization procedure in which the noise variance is set to 10−4 to identify statistically significant coherence. In Figure 5, we showed that significant coherence (P < 0.01) in the simulation (Figure 2) was well captured by our NAIC method. As comparisons, Fourier- and wavelet-based coherence methods were, respectively, performed to analyze the same synthetic data. For wavelet-based coherence, we used the “Morlet” as the mother wavelet (other wavelets yield very similar results). As an example, time-frequency coherence spectra based on the Fourier and wavelet transform between channel X and Z were shown in Figure 6, in which we can see that both coherence spectra exhibit poor time-frequency resolution relative to the proposed NAIC.


Noise-assisted instantaneous coherence analysis of brain connectivity.

Hu M, Liang H - Comput Intell Neurosci (2012)

Decomposition of a synthetic trivariate nonstationary signal [X Y Z] via MEMD. The decomposed three IMFs C1–C3 correctly recover the designed components in the data (Figure 2).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3368308&req=5

fig3: Decomposition of a synthetic trivariate nonstationary signal [X Y Z] via MEMD. The decomposed three IMFs C1–C3 correctly recover the designed components in the data (Figure 2).
Mentions: The MEMD was first performed to decompose the synthetic nonstationary data. Figure 3 showed that the raw data were decomposed into three IMFs, which correctly recovered the designed components in the data (Figure 2), and the common modes within the data were aligned in the IMFs with the same index. By virtue of Hilbert transform, each time series was represented by a time-frequency analytic matrix. A random noise complex matrix with noise variance of 10−4 was then superposed to the analytic matrix of clean data so as to facilitate the calculation of coherence between channels. Figure 4 showed time-frequency coherence based on the mixed data. From this figure, we can see that the obtained time-frequency coherence spectra reflect the designed coupling between channels. We notice, however, that the added noise induces some artifacts, shown as the bright spots scattered in the spectra. We subsequently performed the statistical randomization procedure in which the noise variance is set to 10−4 to identify statistically significant coherence. In Figure 5, we showed that significant coherence (P < 0.01) in the simulation (Figure 2) was well captured by our NAIC method. As comparisons, Fourier- and wavelet-based coherence methods were, respectively, performed to analyze the same synthetic data. For wavelet-based coherence, we used the “Morlet” as the mother wavelet (other wavelets yield very similar results). As an example, time-frequency coherence spectra based on the Fourier and wavelet transform between channel X and Z were shown in Figure 6, in which we can see that both coherence spectra exhibit poor time-frequency resolution relative to the proposed NAIC.

Bottom Line: Characterizing brain connectivity between neural signals is key to understanding brain function.In our method, fully data-driven MEMD, together with Hilbert transform, is first employed to provide time-frequency power spectra for neural data.Furthermore, a statistical randomization procedure is designed to cancel out the effect of the added noise.

View Article: PubMed Central - PubMed

Affiliation: School of Biomedical Engineering, Science & Health Systems, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA.

ABSTRACT
Characterizing brain connectivity between neural signals is key to understanding brain function. Current measures such as coherence heavily rely on Fourier or wavelet transform, which inevitably assume the signal stationarity and place severe limits on its time-frequency resolution. Here we addressed these issues by introducing a noise-assisted instantaneous coherence (NAIC) measure based on multivariate mode empirical decomposition (MEMD) coupled with Hilbert transform to achieve high-resolution time frequency representation of neural coherence. In our method, fully data-driven MEMD, together with Hilbert transform, is first employed to provide time-frequency power spectra for neural data. Such power spectra are typically sparse and of high resolution, that is, there usually exist many zero values, which result in numerical problems for directly computing coherence. Hence, we propose to add random noise onto the spectra, making coherence calculation feasible. Furthermore, a statistical randomization procedure is designed to cancel out the effect of the added noise. Computer simulations are first performed to verify the effectiveness of NAIC. Local field potentials collected from visual cortex of macaque monkey while performing a generalized flash suppression task are then used to demonstrate the usefulness of our NAIC method to provide highresolution time-frequency coherence measure for connectivity analysis of neural data.

Show MeSH
Related in: MedlinePlus