Real-Time dynamics acquisition from irregular samples-With application to anesthesia evaluation

Analysis and Applications

Volumn 14, Issue 4, 2016, Pages 537-590

  Chui, Charles K ^a   Lin, Yu Ting ^b,c   Wu, Hau Tieng ^d  

^a STANFORD UNIVERSITY   (United States)

^b SHIN KONG WU HO SU MEMORIAL HOSPITAL   (Taiwan)

^c NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^d UNIVERSITY OF TORONTO   (Canada)

Author keywords

anesthesia depth; Blending operator; real Time EDR algorithm; real Time time frequency analysis; synchrosqueezing transform; VM wavelet

Indexed keywords

EID: 84948401909     PISSN: 02195305     EISSN: 17936861     Source Type: Journal    
DOI: 10.1142/S0219530515500165     Document Type: Article

References (72)

1. Y. Ait-Sahalia and P. A. Mykland, The effects of random and discrete sampling when estimating continuous time diffusions, Econometrica 71(2) (2003) 483-549.
2. F. Auger, E. Chassande-Mottin and P. Flandrin, Making reassignment adjustable: The Levenberg-Marquardt approach, in 2012 IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan (2012), pp. 3889-3892.
3. F. Auger, P. Flandrin, Y.-T. Lin, S. McLaughlin, S. Meignen, T. Oberlin and H.-T. Wu, Recent advances in time-frequency reassignment and synchrosqueezing, IEEE Trans. Signal Process. 30 (2013) 32-41.
4. R. Baiĺon, L. Sornmo and P. Laguna, ECG derived respiratory frequency estimation, in Advanced Methods and Tools for ECG Data Analysis, eds. G. D. Clifford, F. Azuaje and P. E. McSharry (Artech House, London, 2006), pp. 215-243.
5. G. Benchetrit, Breathing pattern in humans: Diversity and individuality, Resp. Physiol. 122(2-3) (2000) 123-129.
6. J. J Benedetto, Irregular sampling and frames, in Wavelets: A Tutorial in Theory and Applications, ed. C. K. Chui (Academic Press, Boston, 1992), pp. 445-507.
7. I. Bilinskis and A. K. Mikelson, Randomized Signal Processing (Prentice-Hall, 1992).
8. E. Chassande-Mottin, F. Auger and P. Flandrin, Time-frequency/time-scale reassignment, in Wavelets and Signal Processing, Applied and Numerical Harmonic Analysis (Birkhäuser Boston, Boston, MA, 2003), pp. 233-267.
9. E. Chassande-Mottin, I. Daubechies, F. Auger and P. Flandrin, Differential reassignment, IEEE Signal Process. Lett. 4(10) (1997) 293-294.
10. C.-Y. Chen and P. P. Vaidyanathan, Mimo radar space-Time adaptive processing using prolate spheroidal wave functions, IEEE Trans. Signal Process. 56(2) (2008) 623-635.
11. G. Chen, C. K. Chui and M. Lai, Construction of real-Time spline quasi-interpolation schemes, Approx. Appl. 4 (1988) 61-75.
12. Q. Chen, N. Huang, S. Riemenschneider and Y. Xu, A b-spline approach for empirical mode decomposition, Adv. Comput. Math. 24 (2006) 171-195.
13. Y.-C. Chen, M.-Y. Cheng and H.-T. Wu, Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors, J. Roy. Stat. Soc. B 76(3) (2014) 651-682.
14. C. K. Chui, Multivariate Splines (SIAM, 1988).
15. C. K. Chui, An Introduction to Wavelets (Academic Press, 1992).
16. C. K. Chui, Wavelets: A Mathematical Tool for Signal Analysis (SIAM, 1997).
17. C. K. Chui and G. Chen, Kalman Filtering: With Real-Time Applications (Springer, 2009).
18. C. K. Chui and J. M. De Villiers, Applications of optimally local interpolation to interpolatory approximates and compactly supported wavelets, Math. Comp. 213 (1996) 99-114.
19. C. K. Chui and H. Diamond, A general framework to local interpolation, Numer. Math. 58 (1991) 569-581.
20. C. K. Chui and M. J. Lai, Computation of box splines and b-splines on triangulations of nonuniform rectangular partitions, Approx. Theory Appl. 3 (1987) 37-62.
21. C. K. Chui and H. Mhaskar, Signal decomposition and analysis via extraction of frequencies, to appear in Appl. Comput. Harmon. Anal. (2015); dx.doi.org/10.1016/j.acha.2015. 01.003.
22. C. K. Chui and M. van der Walt, Signal analysis via instantaneous frequency estimation of signal components, Int. J. Geomath. 6(1) (2015) 1-42.
23. C. K. Chui and J. Z. Wang, A study of asymptotically optimal time-frequency localization by scaling functions and wavelets, Ann. Numer. Math. 4 (1997) 193-216.
24. I. Daubechies, Ten Lectures on Wavelets (SIAM Philadelphia, PA, 1992).
25. I. Daubechies, J. Lu and H.-T. Wu, Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool, Appl. Comput. Harmon. Anal. (2010) 243-261.
26. I. Daubechies and S. Maes, A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models, in Wavelets in Medicine and Biology, eds. A. Aldroubi and M. Unser (CRC Press, 1996), pp. 527-546.
27. C. de Boor, A Practical Guide to Splines (Springer, 1978).
28. C. de Boor and G. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 8 (1973) 19-45.
29. J. de Villiers, Mathematics of Approximation (Atlantis Press, 2012).
30. Y. C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors, J. Fourier Anal. Appl. 9(1) (2003) 77-96.
31. J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications (Chapman & Hall/CRC, 1996).
32. Z. Feng, X. Chen and M. Liang, Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions, Mech. Syst. Signal Process. 52-53 (2015) 360-375.
33. P. Flandrin, Time-Frequency/Time-Scale Analysis, Wavelet Analysis and Its Applications (Academic Press, 1999).
34. S. Guharay, G. Thakur, F. Goodman, S. Rosen and D. Houser, Analysis of nonstationary dynamics in the financial system, Economics Lett. 121 (2013) 454-457.
35. F. Gunnarsson and F. Gustafsson, Frequency analysis using non-uniform sampling with application to active queue management, in IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP04), Vol. 2, Montreal, Canada (2014), pp. 581-584.
36. L. G. Gurin, B. T. Polyak and E. V. Raik, The method of projections for finding the common point of convex sets, Zh. Vychisl. Mat. Mat. Fiz. 7(6) (1967) 1211-1228.
37. R. H. Herrera, J. Han and M. van der Baan, Applications of the synchrosqueezing transform in seismic time-frequency analysis, Geophysics 79(3) (2014) V55-V64.
38. T. Y. Hou, Z. Shi and P. Tavallali, Sparse time frequency representations and dynamical systems, preprint (2013); arXiv:abs/1312.0202.
39. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung and H. H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A 454(1971) (1998) 903-995.
40. D. Iatsenko, A. Bernjak, T. Stankovski, Y. Shiogai, P. J. Owen-Lynch, P. B. M. Clarkson, P. V. E. McClintock and A. Stefanovska, Evolution of cardiorespiratory interactions with age, Philos. Trans. A Math. Phys. Eng. Sci. 371 (2013) 20110622, 1-18.
41. K. Jacobsson, L. L. H. Andrew, A. K. Tang, S. H. Low and H. Hjalmarsson, An improved link model for window flow control and its application to fast TCP, IEEE Trans. Autom. Control 54(3) (2009) 551-564.
42. M. Kato, T. Komatsu, T. Kimura, F. Sugiyama, K. Nakashima and Y. Shimada, Spectral analysis of heart rate variability during isoflurane anesthesia, Anesthesiology 77 (1992) 669-674.
43. K. Kodera, R. Gendrin and C. Villedary, Analysis of time-varying signals with small bt values, IEEE Trans. Acoust. Speech Signal Process. 26(1) (1978) 64-76.
44. C. Li and M. Liang, Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform, Mech. Syst. Signal Process. 26 (2012) 205-217.
45. P.-C. Li, Y.-L. Sheu, C. Laughlin and S.-I Chu, Role of laser-driven electronmultirescattering in resonance-enhanced below-Threshold harmonic generation in he atoms, Phys. Rev. A. 90 (2013) 041401(R).
46. Y.-T. Lin, H.-T. Wu, J. Tsao, H.-W. Yien and S.-S. Hseu, Time-varying spectral analysis revealing differential effects of sevoflurane anaesthesia: Non-rhythmic-Torhythmic ratio, Acta Anaesthesiol. Scand. 58 (2014) 157-167.
47. N. R. Lomb, Least-squares frequency analysis of unequally spaced data, Astrophys. Space Sci. 39 (1976) 447-462.
48. M. Lustig, D. Donoho and J. M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance Med. 58(6) (2007) 1182-1195.
49. T. Lyche and L. L. Schumaker, Local spline approximation, J. Approx. Theory 15 (1975) 294-325.
50. M. J. Marsden, An identity for spline functions with applications to variationdiminishing spline approximation, J. Approx. Theory 3 (1970) 7-49.
51. F. Marvasti, Nonuniform Sampling: Theory and Practice (Springer, 2001).
52. C. A. Micchelli, Y. Xu and B. Yu, On computing with the Hilbert spline transform, Adv. Comput. Math. 38 (2013) 623-646.
53. R. A. Mitchell and A. J. Berger, Neural regulation of respiration, Am. Rev. Respir. Dis. 111 (1975) 206-224.
54. G. B. Moody, Spectral analysis of heart rate without resampling, in Proc. IEEE Computers in Cardiology, London, UK (1993), pp. 715-718.
55. G. B. Moody, R. G. Mark, A. Zoccola and S. Mantero, Derivation of respiratory signals from multi-lead ECGS, Comput. Cardiol. 12 (1985) 113-116.
56. J. C. Rekling and J. L. Feldman, PreBötzinger complex and pacemaker neurons: Hypothesized site and kernel for respiratory rhythm generation, Ann. Rev. Physiol. 60 (1998) 385-405.
57. L. L. Schumaker, Spline Functions: Basic Theory (Wiley-Interscience, 1981).
58. W. D. Smith, R. C. Dutton and N. T. Smith, Measuring the performance of anesthetic depth indicators, Anesthesiology 84 (1996) 38-51.
59. M. Soehle, R. K. Ellerkmann, M. Grube, M. Kuech, S. Wirz, A. Hoeft and J. Bruhn, Comparison between bispectral index and patient state index as measures of the electroencephalographic effects of sevoflurane, Anesthesiology 109 (2008) 799-805.
60. V. K. Somers, D. P. White, R. Amin, W. T. Abraham, F. Costa, A. Culebras, S. Daniels, J. S. Floras, C. E. Hunt, L. J. Olson, T. G. Pickering, R. Russell, M. Woo and T. Young, Sleep apnea and cardiovascular disease: An American Heart Association/American College of Cardiology Foundation Scientific Statement from the American Heart Association Council for High Blood Pressure Research Professional Education Committee, Council on Clinical Cardiology, Stroke Council, and Council on Cardiovascular Nursing, J. Am. Coll. Cardiol. 52(8) (2008) 686-717.
61. G. Thakur and H.-T. Wu, Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples, SIAM J. Math. Anal. 43 (2011) 2078-2095.
62. M. van der Walt, Wavelet analysis of non-stationary signals with applications, Ph.D.Thesis, University Missouri-St. Louis (2015).
63. T. Vatter, H.-T. Wu, V. Chavez-Demoulin and B. Yu, Non-parametric estimation of intraday spot volatility: Disentangling instantaneous trend and seasonality, SSRN e-prints (2013) 2330159.
64. R. Vio, T. Strohmer and W. Wamsteker, On the reconstruction of irregularly sampled time series, Publ. Astron. Soc. Pacific 112(767) (2000) 74-90.
65. P. Wang, J. Gao and Z. Wang, Time-frequency analysis of seismic data using synchrosqueezing transform, Geosci. Remote Sens. Lett. 11(12) (2014) 2042-2044.
66. H.-T. Wu, Adaptive analysis of complex data sets, Ph.D.Thesis, Princeton University (2011).
67. H.-T. Wu, Instantaneous frequency and wave shape functions (I), Appl. Comput. Harmon. Anal. 35 (2013) 181-199.
68. H.-T. Wu, Y.-H. Chan, Y.-T. Lin and Y.-H. Yeh, Using synchrosqueezing transform to discover breathing dynamics from ECG signals, Appl. Comput. Harmon. Anal. 36 (2014) 354-359.
69. H.-T. Wu, S.-S. Hseu, M.-Y. Bien, Y. R. Kou and I. Daubechies, Evaluating physiological dynamics via synchrosqueezing: Prediction of ventilator weaning, IEEE Trans. Biomedical Eng. 61 (2013) 736-744.
70. H.-T. Wu, R. Talmon and Y.-L. Lo, Assess sleep stage by modern signal processing techniques, IEEE Trans. Biomedical Eng. 62(4) (2015) 1159-1168.
71. M. Wysocki, C. Cracco, A. Teixeira, A. Mercat, J. Diehl, Y. Lefort, J. Derenne and T. Similowski, Reduced breathing variability as a predictor of unsuccessful patient separation from mechanical ventilation, Crit. Care Med. 34 (2006) 2076-2083.
72. H. Yang, Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions, to appear in Appl. Comput. Harmon. Anal.