A time-frequency-based approach to phase and phase synchrony estimation

IEEE Transactions on Signal Processing

Volumn 59, Issue 7, 2011, Pages 3086-3098

  Aviyente, Selin ^a   Mutlu, Ali Yener ^a  

^a Michigan State University   (United States)

Author keywords

Phase estimation; phase synchrony; Rihaczek distribution; time frequency analysis

Indexed keywords

BIVARIATE; CHAOTIC OSCILLATORS; COHEN'S CLASS; COMPLEX WAVELET TRANSFORMS; FREQUENCY DEPENDENT; HILBERT TRANSFORM; MULTI-CHANNEL; NARROW BANDS; NONSTATIONARY SIGNALS; PHASE ESTIMATION; PHASE ESTIMATORS; PHASE SYNCHRONY; RIHACZEK DISTRIBUTION; TIME FREQUENCY ANALYSIS; TIME VARYING; TIME-FREQUENCY RESOLUTION;

CIRCUIT OSCILLATIONS; ELECTROPHYSIOLOGY; ESTIMATION; IMAGE SEGMENTATION; TIME VARYING SYSTEMS; WAVELET ANALYSIS; WAVELET TRANSFORMS;

FREQUENCY ESTIMATION;

EID: 79959200863     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2144589     Document Type: Article

References (41)

1. M. Le Van Quyen, J. Foucher, J. P. Lachaux, E. Rodriguez, A. Lutz, J. Martinerie, and F. J. Varela, "Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony," J. Neurosci. Methods, vol. 111, no. 2, pp. 83-98, 2001. (Pubitemid 32930045)
2. R. Sneyers, "Climate chaotic instability: Statistical determination and theoretical background," Environmetrics, vol. 8, no. 5, pp. 517-532, 1997. (Pubitemid 27439719)
3. C. Kyrtsou and W. Labys, "Detecting positive feedback in multivariate time series: The case of metal prices and us inflation," Physica A: Statist. Mechan. Appl., vol. 377, no. 1, pp. 227-229, 2007. (Pubitemid 46108451)
4. M. Hasler, "Engineering chaos for encryption and broadband communication," Philosoph. Trans. A, vol. 353, no. 1701, pp. 115-126, 1995.
5. M. G. Rosenblum, A. A. Pikovsky, and J. Kurths, "Phase synchronization of chaotic oscillators," Phys. Rev. Lett., vol. 76, no. 11, pp. 1804-1807, 1996. (Pubitemid 126638871)
6. P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H. J. Freund, "Detection of n: m phase locking from noisy data: Application to magnetoencephalography," Phys. Rev. Lett., vol. 81, no. 15, pp. 3291-3294, 1998. (Pubitemid 128629556)
7. J. P. Lachaux, A. Lutz, D. Rudrauf, D. Cosmelli, M. Le Van Quyen, J. Martinerie, and F. Varela, "Estimating the time-course of coherence between single-trial brain signals: An introduction to wavelet coherence," Neurophysiol. Clin./Clin. Neurophysiol., vol. 32, no. 3, pp. 157-174, 2002. (Pubitemid 34790482)
8. N. Huang, Z. Shen, S. Long, M. Wu, H. Shih, Q. Zheng, N. Yen, C. Tung, and H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis," Proc.: Math., Phys. Eng. Sci., vol. 454, no. 1971, pp. 903-995, 1998. (Pubitemid 128733183)
9. C. Sweeney-Reed and S. Nasuto, "A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition," J. Computat. Neurosci., vol. 23, no. 1, pp. 79-111, 2007. (Pubitemid 47422588)
10. D. Li and R. Jung, "Quantifying coevolution of nonstationary biomedical signals using time-varying phase spectra," Ann. Biomed. Eng., vol. 28, no. 9, pp. 1101-1115, 2000. (Pubitemid 32085798)
11. S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 674-693, 1989.
12. K. Göchenig, Foundations of Time-Frequency Analysis. Boston, MA: Birkhäuser, 2001.
13. L. Angelini, M. D. Tommaso, M. Guido, K. Hu, P. C. Ivanov, D. Marinazzo, G. Nardulli, L. Nitti, M. Pellicoro, C. Pierro, and S. Stramaglia, "Steady-state visual evoked potentials and phase synchronization in migraine patients," Phys. Rev. Lett., vol. 93, no. 3, p. 38103, 2004.
14. J. Bhattacharya, "Reduced degree of long-range phase synchrony in pathological human brain," Acta Neurobiologiae Experimentalis, vol. 61, no. 4, pp. 309-318, 2001. (Pubitemid 34074308)
15. M. Koskinen, T. Seppänen, J. Tuukkanen, A. Yli-Hankala, and V. Jäntti, "Propofol anesthesia induces phase synchronization changes in EEG," Clin. Neurophysiol., vol. 112, no. 2, pp. 386-392, 2001. (Pubitemid 32126475)
16. C. Ioana and A. Quinquis, "Time-frequency analysis using warped-based high-order phase modeling," EURASIP J. Appl. Signal Process., vol. 17, pp. 2856-2873, 2005. (Pubitemid 44178266)
17. B. Porat, Digital Processing of Random Signals: Theory and Methods. Englewood Cliffs, NJ: Prentice-Hall, 1994.
18. S. Barbarossa, A. Scaglione, and G. Giannakis, "Product high-order ambiguity function for multicomponent polynomial-phase signal modeling," IEEE Trans. Signal Process., vol. 46, no. 3, pp. 691-708, 1998. (Pubitemid 128743774)
19. J. Eckmann, S. O. Kamphorst, and D. Ruelle, "Recurrence plots of dynamical systems," EPL (Europhys. Lett.), vol. 4, pp. 973-977, 1987.
20. J. Zbilut, A. Giuliani, and C. Webber, "Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification," Phys. Lett. A, vol. 246, no. 1, pp. 122-128, 1998. (Pubitemid 128399554)
21. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, "Recurrence plots for the analysis of complex systems," Phys. Rep., vol. 438, no. 5-6, pp. 237-329, 2007.
22. S. Aviyente, E. Bernat, W. Evans, and S. Sponheim, "A phase synchrony measure for quantifying dynamic functional integration in the brain," Human Brain Mapping, 2010.
23. E. Pereda, R. Quiroga, and J. Bhattacharya, "Nonlinear multivariate analysis of neurophysiological signals," Progress in Neurobiol., vol. 77, no. 1-2, pp. 1-37, 2005. (Pubitemid 41654771)
24. T. Kreuz, R. Andrzejak, F. Mormann, A. Kraskov, H. Stögbauer, C. Elger, K. Lehnertz, and P. Grassberger, "Measure profile surrogates: A method to validate the performance of epileptic seizure prediction algorithms," Phys. Rev. E, vol. 69, no. 6, p. 61915, 2004.
25. L. Cohen, Time-Frequency Analysis: Theory and Applications. Englewood Cliffs, NJ: Prentice-Hall, 1995.
26. J. Jeong and W. Williams, "Kernel design for reduced interference distributions," IEEE Trans. Signal Process., vol. 40, pp. 402-412, 1992.
27. A. Rihaczek, "Signal energy distribution in time and frequency," IEEE Trans. Inf. Theory, vol. 14, no. 3, pp. 369-374, 1968.
28. P. Schreier, L. Scharf, and A. Hanssen, "A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals," in Proc. Int. Symp. Inf. Theory (ISIT), 2005, pp. 966-969.
29. L. Scharf, B. Friedlander, P. Flandrin, and A. Hanssen, "The Hilbert space geometry of the stochastic Rihaczek distribution," in Proc. Asilomar Conf. Signals Syst. Comput., 2001, vol. 1, pp. 720-725. (Pubitemid 34244727)
30. B. Gillespie and L. Atlas, "Optimizing time-frequency kernels for classification," IEEE Trans. Signal Process., vol. 49, no. 3, pp. 485-496, 2001. (Pubitemid 32583151)
31. J. O'neill and W. Williams, "Shift covariant time-frequency distributions of discrete signals," IEEE Trans. Signal Process., vol. 47, no. 1, pp. 133-146, 1999.
32. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993, ch. 15, pp. 45-525.
33. A. Hero, III, J. Fessler, and M. Usman, "Exploring estimator biasvariance tradeoffs using the uniform CR bound," IEEE Trans. Signal Process., vol. 44, no. 8, pp. 2026-2041, 1996. (Pubitemid 126778023)
34. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, "Testing for nonlinearity in time series: The method of surrogate data," Physica D: Nonlin. Phenom., vol. 58, no. 1-4, pp. 77-94, 1992.
35. G. Tcheslavski, "Coherence and phase synchrony analysis of electroen-cephalogram," Ph.D. dissertation, Virginia Polytech. Inst. State Univ., Blacksburg, 2005, Ch. 3, p. 46.
36. Y. Kuramoto, "Self-entrainment of a population of coupled nonlinear oscillators," in Proc. Int. Symp. Math. Problems in Theoret. Phys., Lecture Notes in Phys., 1975, vol. 39, pp. 420-422.
37. S. Strogatz, "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Phys. D: Nonlin. Phenom., vol. 143, no. 1-4, pp. 1-20, 2000.
38. J. Acebrón, L. Bonilla, C. P. Vicente, F. Ritort, and R. Spigler, "The Kuramoto model: A simple paradigm for synchronization phenomena," Rev. Modern Phys., vol. 77, no. 1, pp. 137-185, 2005. (Pubitemid 41490657)
39. M. Yeung and S. Strogatz, "Time delay in the Kuramoto model of coupled oscillators," Phys. Rev. Lett., vol. 82, no. 3, pp. 648-651, 1999. (Pubitemid 129571687)
40. C. Stam, G. Nolte, and A. Daffertshofer, "Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources," Human Brain Mapping, vol. 28, no. 11, pp. 1178-1193, 2007. (Pubitemid 350077482)
41. N. Rehman and D. Mandic, "Multivariate empirical mode decomposition," Proc. Royal Soc. London, Ser. A: Math., Phys. Eng. Sci., vol. 466, no. 2117, pp. 1291-1302, 2010.