Adaptive data analysis via sparse time-frequency representatioN

Advances in Adaptive Data Analysis

Volumn 3, Issue 1-2, 2011, Pages 1-28

  Hou, Thomas Y ^a   Shi, Zuoqiang ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

empirical mode decomposition; instantaneous frequency; L1 minimization; sparse representation of signal; Time frequency analysis

Indexed keywords

EMPIRICAL MODE DECOMPOSITION; INSTANTANEOUS FREQUENCY; L1 MINIMIZATION; SPARSE REPRESENTATION; TIME FREQUENCY ANALYSIS;

ADAPTIVE FILTERS; ALGORITHMS; DATA REDUCTION; NONLINEAR ANALYSIS; OPTIMIZATION;

NUMERICAL METHODS;

EID: 80052641966     PISSN: 17935369     EISSN: 17937175     Source Type: Journal    
DOI: 10.1142/S1793536911000647     Document Type: Conference Paper

References (33)

1. Bedrosian, E. (1963). A product theorem for Hilbert transforms. Proc. IEEE., 51: 868-869.
2. Boashash, B. (1992) Time Frequency Signal Analysis Methods and Applications, Longman-Cheshire, Melbourne and John Wiley Halsted Press, New York.
3. Bruckstein, A. M., Donoho, D. L. and Elad, M. (2009). From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev., 51: 34-81.
4. Cand̀es, E. and Tao, T. (2006). Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory, 52(12): 5406-5425. (Pubitemid 46445381)
5. Candes, E. Romberg, J. and Tao, T. (2006a). Robust uncertainty principles: Exact signal recovery from highly incomplete frequency information. IEEE Trans. Inf. Theory, 52: 489-509. (Pubitemid 43174093)
6. Candes, E., Romberg, J. and Tao, T. (2006b). Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math., 59: 1207-1223. (Pubitemid 43988295)
7. Cohen, L. (1995). Time-Frequency Analysis, Prentice Hall, Englewood Cliffs, NJ.
8. Daubechies, I., (1992). Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series on Applied Mathematics, Vol. 61, SIAM Publications.
9. Daubechiesa, I. Lu, J. and Wu, H.-T. (2011). Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 30(2): 243-261.
10. Donoho, D. L. (2006). Compressed sensing. IEEE Trans. Inf. Theory, 52: 1289-1306.
11. Flandrin, P. (1999). Time-Frequency/Time-Scale Analysis, Academic Press, San Diego, CA.
12. Gabor, D. (1946). Theory of communication. J. IEE., 93: 426-457.
13. Goldstein, T. and Osher, S. (2009). The split Bregman method for L-regularized problems. SIAM J. Imaging Sci. 2(2): 323-343.
14. Hou, T. Y. and Shi, Z. (2011). Sparse time-frequency representation of multiscale data by nonlinear matching pursuit. SIAM Multiscale Model. Sim., submitted.
15. Huang, N. E. et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Londn. A, 454: 903-995. (Pubitemid 128733183)
16. Huang, N. E., Shen, Z. and Long, S. R. (1999). A new view of nonlinear water waves-The Hilbert spectrum. Ann. Rev. Fluid Mech., 31: 417-457. (Pubitemid 36186209)
17. Huang, N. E., Wu, Z., Long, S. R., Arnold, K. C, Chen, X. and Blank, K. (2009). On instantaneous frequency. Adv. Adapt. Data Anal. 1(2): 177-229.
18. Jomes, D. L. and Parks, T. W. (1990). A high resolution data-adaptive time-frequency representation. IEEE Trans. Acoust. Speech Signal Process., 38: 2127-2135.
19. Kim, S. J., Koh, K., Lustig, M., Boyd, S. and Gorinevsky, D. (2007). An interior-point method for large-scale L-regularized least squares. IEEE J. Sel. Top. Signal Process., 1(4): 606-617. (Pubitemid 351266626)
20. Loughlin, P. J. and Tracer, B. (1996). On the amplitude-and frequency-modulation decomposition of signals. J. Acoust. Soc. Am., 100: 1594-1601.
21. Lovell, B. C., Williamson, R. C. and Boashash, B. (1993). The relationship between instantaneous frequency and time frequency representations. IEEE Trans. Signal Process., 41(3): 1458-1461. (Pubitemid 23701020)
22. Mallat, S. (2009). A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, San Diego, CA.
23. Meville, W. K. (1983). Wave modulation and breakdown. J. Fluid Mech., 128: 489-506.
24. Nuttall, A. H. (1966). On the quadrature approximation to the Hilbert transform of modulated signals. Proc. IEEE., 54: 1458-1459.
25. Olhede, S. and Walden, A. T. (2004). The Hilbert spectrum via wavelet projections. Proc. Roy. Soc. Lond. A, 460: 955-975. (Pubitemid 38406356)
26. Picinbono, B. (1997). On instantaneous amplitude and phase signals. IEEE Trans. Signal Process., 45: 552-560.
27. Qian, S. and Chen, D. (1996). Joint Time-Frequency Analysis: Methods and Applications, Prentice Hall, Englewood Cliffs, NJ.
28. Rice, S. O. (1944). Mathematical analysis of random noise. Bell Syst. Tech. J., 23: 282-310.
29. Shekel, J. (1953). Instantaneous frequency. Proc. IRE, 41: 548-548.
30. Van der Pol, B. (1946). The fundamental principles of frequency modulation. Proc. IEEE, 93: 153-158.
31. Wu, Z. and Huang, N. E. (2005). Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method, COLA Technical Report 193. ftp://grads.iges.org/pub/ctr/ctr-193.pdf.
32. Wu, Z., Huang, N. E., Long, S. R. and Peng, C. K. (2007). Trend, detrend, and the variability of nonlinear and non-stationary time series. Proc. Natl. Acad. Sci. USA., 104: 14889-14894. doi: 10.1073/pnas.0701020104. (Pubitemid 47619564)
33. Wu, Z. and Huang, N. E. (2009). Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv. Adapt. Data Anal. 1(1): 1-41.