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. 1. Introduction To understand how brain networks process information, it is crucial to accurately quantify their connectivity patterns. For analysis of brain connectivity between two signals, current measures such as coherence [1–3] rely upon spectral estimate of each signal, which is routinely computed based on Fourier or wavelet transform. Thus, the underlying nonstationary nature of neural data presents a significant challenge for the applications of current measures. Though short-time sliding window approaches, for example, short-time Fourier transform, have been used to alleviate this problem, this issue is not completely resolved for a number of reasons. First, the stationarity of neural data within each short-time window cannot be guaranteed. Second, even though the data are stationary within each time window, the resolution of time-frequency representation is limited by Heisenberg uncertainty principle [4]. Wavelet transform [4], albeit improved, is still subject to time-frequency resolution tradeoff, that is, frequency resolution is low at high frequencies and high at low frequencies. Moreover, wavelet analysis depends on
G. G. Gregoriou, S. J. Gotts, H. Zhou, and R. Desimone, “High-Frequency, long-range coupling between prefrontal and visual cortex during attention,” Science, vol. 324, no. 5931, pp. 1207–1210, 2009.
H. Liang, S. L. Bressler, M. Ding, R. Desimone, and P. Fries, “Temporal dynamics of attention-modulated neuronal synchronization in macaque V4,” Neurocomputing, vol. 52–54, pp. 481–487, 2003.
A. Brovelli, M. Ding, A. Ledberg, Y. Chen, R. Nakamura, and S. L. Bressler, “Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 26, pp. 9849–9854, 2003.
N. E. Huang, Z. Shen, S. R. Long et al., “The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society A, vol. 454, no. 1971, pp. 903–993, 1998.
M. Altaf, T. Gautama, T. Tanaka, and D. P. Mandic, “Rotation invariant complex empirical mode decomposition,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '07), pp. 1009–1012, Honolulu, Hawaii, USA, April 2007.
G. Rilling, P. Flandrin, P. Goncalves, and J. M. Lilly, “Bivariate empirical mode decomposition,” IEEE Signal Processing Letters, vol. 14, no. 12, pp. 936–939, 2007.
N. Rehman and D. P. Mandic, “Empirical mode decomposition for trivariate signals,” IEEE Transaction on Signal Processing, vol. 58, pp. 1059–1068, 2010.
Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition method,” Advances in Adaptive Data Analysis, vol. 1, pp. 339–372, 2009.
N. Rehman and D. P. Mandic, “Filter bank property of multivariate empirical mode decomposition,” IEEE Transactions on Signal Processing, vol. 59, no. 5, pp. 2421–2426, 2011.
M. Hu and H. Liang, “Adaptive multiscale entropy analysis of multivariate neural data,” IEEE Transactions on Biomedical Engineering, vol. 59, no. 1, pp. 12–15, 2011.
M. Hu and H. Liang, “Intrinsic mode entropy based on multivariate empirical mode decomposition and its application to neural data analysis,” Cognitive Neurodynamics, vol. 5, no. 3, pp. 277–284, 2011.
M. Dhamala, G. Rangarajan, and M. Ding, “Analyzing information flow in brain networks with nonparametric Granger causality,” NeuroImage, vol. 41, no. 2, pp. 354–362, 2008.
W. J. Freeman, “Origin, structure, and role of background EEG activity—part 1. Analytic amplitude,” Clinical Neurophysiology, vol. 115, no. 9, pp. 2077–2088, 2004.
M. Kaminski and H. Liang, “Causal influence: advances in neurosignal analysis,” Critical Reviews in Biomedical Engineering, vol. 33, no. 4, pp. 347–430, 2005.
E. Maris and R. Oostenveld, “Nonparametric statistical testing of EEG- and MEG-data,” Journal of Neuroscience Methods, vol. 164, no. 1, pp. 177–190, 2007.
Z. Wang, A. Maier, D. A. Leopold, N. K. Logothetis, and H. Liang, “Single-trial evoked potential estimation using wavelets,” Computers in Biology and Medicine, vol. 37, no. 4, pp. 463–473, 2007.
M. Wilke, N. K. Logothetis, and D. A. Leopold, “Local field potential reflects perceptual suppression in monkey visual cortex,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 46, pp. 17507–17512, 2006.
D. Maraun, J. Kurths, and M. Holschneider, “Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing,” Physical Review E, vol. 75, no. 1, Article ID 016707, 2007.
D. Maraun and J. Kurths, “Cross wavelet analysis: significance testing and pitfalls,” Nonlinear Processes in Geophysics, vol. 11, no. 4, pp. 505–514, 2004.
P. Flandrin, G. Rilling, and P. Goncalves, “Empirical mode decomposition as a filter bank,” IEEE Signal Processing Letters, vol. 11, no. 2, pp. 112–114, 2004.
Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proceedings of the Royal Society A, vol. 460, no. 2046, pp. 1597–1611, 2004.
P. Flandrin, P. Goncalves, and G. Rilling, “EMD equivalent filter banks, from interpretation to applications,” in Hilbert-Huang Transform : Introduction and Applications, World Scientific, Singapore, 2005.
Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Advances in Adaptive Data Analysis, vol. 1, pp. 1–41, 2009.
C. M. Sweeney-Reed and S. J. Nasuto, “A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition,” Journal of Computational Neuroscience, vol. 23, no. 1, pp. 79–111, 2007.
M. Palus and A. Stefanovska, “Direction of coupling from phases of interacting oscillators: an information-theoretic approach,” Physical Review E, vol. 67, no. 5, Article ID 055201, 2003.
M. G. Rosenblum and A. S. Pikovsky, “Detecting direction of coupling in interacting oscillators,” Physical Review E, vol. 64, no. 4, Article ID 045202R, 2001.
M. Palus, D. Novotna, and P. Tichavsky, “Shifts of seasons at the European mid-latitudes: natural fluctuations correlated with the North Atlantic Oscillation,” Geophysical Research Letters, vol. 32, Article ID L12805, 2005.