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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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Schematic representation of the proposed noise-assisted instantaneous coherence (NAIC). A trivariate data [X Y Z] is used as an example. The first step (A) consists of transforming each time series to the corresponding analytic matrix by virtue of the MEMD and Hilbert transform. A random noise complex matrix is then added to the analytic matrix of data (B) to facilitate the calculation of coherence (C). Two random noise complex matrices are independently generated to compute their coherence. The process is repeated for N (e.g., 1000) times (D) to obtain a  distribution of the maximum coherence (E). Here, we set the P value as 0.01, thus the threshold “T” corresponds to the 10th value from the maximum of the  distribution (F). Finally, we use the “T” to threshold the coherence from (C) to be considered as statistically significant from noise (G). The output of NAIC (H) provides high-resolution time-frequency coherence spectrum.
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fig1: Schematic representation of the proposed noise-assisted instantaneous coherence (NAIC). A trivariate data [X Y Z] is used as an example. The first step (A) consists of transforming each time series to the corresponding analytic matrix by virtue of the MEMD and Hilbert transform. A random noise complex matrix is then added to the analytic matrix of data (B) to facilitate the calculation of coherence (C). Two random noise complex matrices are independently generated to compute their coherence. The process is repeated for N (e.g., 1000) times (D) to obtain a distribution of the maximum coherence (E). Here, we set the P value as 0.01, thus the threshold “T” corresponds to the 10th value from the maximum of the distribution (F). Finally, we use the “T” to threshold the coherence from (C) to be considered as statistically significant from noise (G). The output of NAIC (H) provides high-resolution time-frequency coherence spectrum.

Mentions: Conventional coherence methods based on Fourier transform or autoregressive model assume that input signals are stationary, and their time-frequency representations suffer from the fundamental uncertainty principle. In this study, we propose a noise-assisted instantaneous coherence, which is suited to the analysis of nonstationary neural signals and offers high-resolution time-frequency coherence estimate. A schematic representation of the processing steps is shown in Figure 1.


Noise-assisted instantaneous coherence analysis of brain connectivity.

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

Schematic representation of the proposed noise-assisted instantaneous coherence (NAIC). A trivariate data [X Y Z] is used as an example. The first step (A) consists of transforming each time series to the corresponding analytic matrix by virtue of the MEMD and Hilbert transform. A random noise complex matrix is then added to the analytic matrix of data (B) to facilitate the calculation of coherence (C). Two random noise complex matrices are independently generated to compute their coherence. The process is repeated for N (e.g., 1000) times (D) to obtain a  distribution of the maximum coherence (E). Here, we set the P value as 0.01, thus the threshold “T” corresponds to the 10th value from the maximum of the  distribution (F). Finally, we use the “T” to threshold the coherence from (C) to be considered as statistically significant from noise (G). The output of NAIC (H) provides high-resolution time-frequency coherence spectrum.
© Copyright Policy
Related In: Results  -  Collection

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

fig1: Schematic representation of the proposed noise-assisted instantaneous coherence (NAIC). A trivariate data [X Y Z] is used as an example. The first step (A) consists of transforming each time series to the corresponding analytic matrix by virtue of the MEMD and Hilbert transform. A random noise complex matrix is then added to the analytic matrix of data (B) to facilitate the calculation of coherence (C). Two random noise complex matrices are independently generated to compute their coherence. The process is repeated for N (e.g., 1000) times (D) to obtain a distribution of the maximum coherence (E). Here, we set the P value as 0.01, thus the threshold “T” corresponds to the 10th value from the maximum of the distribution (F). Finally, we use the “T” to threshold the coherence from (C) to be considered as statistically significant from noise (G). The output of NAIC (H) provides high-resolution time-frequency coherence spectrum.
Mentions: Conventional coherence methods based on Fourier transform or autoregressive model assume that input signals are stationary, and their time-frequency representations suffer from the fundamental uncertainty principle. In this study, we propose a noise-assisted instantaneous coherence, which is suited to the analysis of nonstationary neural signals and offers high-resolution time-frequency coherence estimate. A schematic representation of the processing steps is shown in Figure 1.

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