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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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Root mean square error (RMSE) between the estimated coherence and its theoretical value as a function of the noise variance. Error bars denote standard deviations over 50 repetitions. Note that the RMSE declined as the noise variance decreased and stayed constant once the noise variance approaches 10−4.
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fig7: Root mean square error (RMSE) between the estimated coherence and its theoretical value as a function of the noise variance. Error bars denote standard deviations over 50 repetitions. Note that the RMSE declined as the noise variance decreased and stayed constant once the noise variance approaches 10−4.

Mentions: In our NAIC approach, an important question is how much noise is acceptable. To examine the effect of noise on coherence estimation, we systematically varied the noise by changing its variance relative to the signal and estimated the coherence between channel X and Z in the above simulation. We measured the root mean square error (RMSE) [23] between the estimated coherence and its theoretical value as a function of noise variance. We repeated the same analysis procedure for 50 times to obtain error bars at each noise level. The result is shown in Figure 7. We can see from the figure that the RMSE declined as the noise variance decreased, and stayed constant when the noise variance approaches 10−4. While the amount of noise derived from this particular simulation is empirical, it indicates that the amount of noise should be four orders of magnitude less than the signal. As a rule of thumb, we suggest that the added noise should be of infinitesimal magnitude so as to minimize the interaction between the added noise and original clean signal.


Noise-assisted instantaneous coherence analysis of brain connectivity.

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

Root mean square error (RMSE) between the estimated coherence and its theoretical value as a function of the noise variance. Error bars denote standard deviations over 50 repetitions. Note that the RMSE declined as the noise variance decreased and stayed constant once the noise variance approaches 10−4.
© Copyright Policy
Related In: Results  -  Collection

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

fig7: Root mean square error (RMSE) between the estimated coherence and its theoretical value as a function of the noise variance. Error bars denote standard deviations over 50 repetitions. Note that the RMSE declined as the noise variance decreased and stayed constant once the noise variance approaches 10−4.
Mentions: In our NAIC approach, an important question is how much noise is acceptable. To examine the effect of noise on coherence estimation, we systematically varied the noise by changing its variance relative to the signal and estimated the coherence between channel X and Z in the above simulation. We measured the root mean square error (RMSE) [23] between the estimated coherence and its theoretical value as a function of noise variance. We repeated the same analysis procedure for 50 times to obtain error bars at each noise level. The result is shown in Figure 7. We can see from the figure that the RMSE declined as the noise variance decreased, and stayed constant when the noise variance approaches 10−4. While the amount of noise derived from this particular simulation is empirical, it indicates that the amount of noise should be four orders of magnitude less than the signal. As a rule of thumb, we suggest that the added noise should be of infinitesimal magnitude so as to minimize the interaction between the added noise and original clean signal.

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