Determining local singularity strengths and their spectra with the wavelet transform

Fractals

Volumn 8, Issue 2, 2000, Pages 163-179

  Struzik, Zbigniew R ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042962875     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X00000184     Document Type: Article

References (30)

1. A. Arneodo, E. Bacry and J. F. Muzy, "Wavelets and Multifractal Formalism for Singular Signals: Application to Turbulence Data," PRL 67, 3515-3518 (1991).
2. 2. A. Arneodo, E. Bacry and J. F. Muzy, "The Thermodynamics of Fractals Revisited with Wavelets," Physica A213, 232-275 1995; J. F. Muzy, E. Bacry and A. Arneodo, "The Multifractal Formalism Revisited with Wavelets," Int. J. Bifurc. Chaos 4, 245-302 (1994).
3. A. Arneodo, E. Bacry and J. F. Muzy, "The Thermodynamics of Fractals Revisited with Wavelets," Physica A213, 232-275 1995; J. F. Muzy, E. Bacry and A. Arneodo, "The Multifractal Formalism Revisited with Wavelets," Int. J. Bifurc. Chaos 4, 245-302 (1994).
4. A. Arneodo, A. Argoul, J. F. Muzy, M. Tabard and E. Bacry, "Beyond Classical Multifractal Analysis Using Wavelets: Uncovering a Multiplicative Process Hidden in the Geometrical Complexity of Diffusion Limited Aggregates," Fractals 1, 629-646 (1995).
5. A. Arneodo, E. Bacry, P. V. Graves and J. F. Muzy, "Characterizing Long-Range Correlations in DNA Sequences from Wavelet Analysis," PRL 74, 3293-3296 (1995).
6. P. Ch. Ivanov, M. G. Rosenblum, C.-K. Peng, J. Mietus, S. Havlin, H. E. Stanley and A. L. Goldberger, "Scaling Behaviour of Heartbeat Intervals Obtained by Wavelet-Based Time Series Analysis," Nature 383, 323-327 (1996).
7. P. Ch. Ivanov, M. G. Rosenblum, L. A. Nunes Amaral, Z. R. Struzik, S. Havlin, A. L. Goldberger and H. E. Stanley, "Multifractality in Human Heartbeat Dynamics," Nature 399, 461-465 (1999).
8. 7. Z. R. Struzik, "The Wavelet Transform in the Solution to the Inverse Fractal Problem," Fractals 3(2), 329-350 (1995); Z. R. Struzik, From Coastline Length to Inverse Fractal Problem: The Concept of Fractal Metrology, Thesis (University of Amsterdam, 1996).
9. Z. R. Struzik, "The Wavelet Transform in the Solution to the Inverse Fractal Problem," Fractals 3(2), 329-350 (1995); Z. R. Struzik, From Coastline Length to Inverse Fractal Problem: The Concept of Fractal Metrology, Thesis (University of Amsterdam, 1996).
10. Z. R. Struzik, "Local Effective Hölder Exponent Estimation on the Wavelet Transform Maxima Tree," in Fractals: Theory and Applications in Engineering, eds. M. Dekking, J. Lévy Véhel, E. Lutton, C. Tricot (Springer Verlag, 1999), pp. 93-112.
11. I. Daubechies, Ten Lectures On Wavelets (S.I.A.M., 1992).
12. M. Holschneider, Wavelets - An Analysis Tool (Oxford Science Publications, 1995).
13. S. Jaffard and Y. Meyer, "Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions," Memoirs of AMS, Vol. 123, No. 587 (1996).
14. B. Guiheneuf and J. Lévy Véhel, "2-Microlocal Analysis and Application in Signal Processing," in Proc. Int. Wavelets Conference, Tangier (1998).
15. S. Jaffard, "Multifractal Formalism for Functions: I. Results Valid for all Functions, II. Self-Similar Functions," SIAM J. Math. Anal. 28(4), 944-998 (1997).
16. A. Arneodo, E. Bacry and J. F. Muzy, "Oscillating Singularities in Locally Self-Similar Functions," PRL 74(24), 4823-4826 (1995).
17. S. G. Mallat and W. L. Hwang, "Singularity Detection and Processing with Wavelets," IEEE Trans. Information Theory 38, 617-643 (1992).
18. S. G. Mallat and S. Zhong, "Complete Signal Representation with Multiscale Edges," IEEE Trans. PAMI 14, 710-732 (1992).
19. A. Arneodo, E. Bacry and J. F. Muzy, "Solving the Inverse Fractal Problem from Wavelet Analysis," Europhysics Letters 25(7), 479-484 (1994).
20. 18. Z. R. Struzik, "Removing Divergences in the Negative Moments of the Multi-Fractal Partition Function with the Wavelet Transformation," CWI Report, INS-R9803 (1998). See also Fractals and Beyond - Complexities in the Sciences, ed. M. M. Novak (World Scientific, 1998), pp. 351-352.
21. Z. R. Struzik, "Removing Divergences in the Negative Moments of the Multi-Fractal Partition Function with the Wavelet Transformation," CWI Report, INS-R9803 (1998). See also Fractals and Beyond - Complexities in the Sciences, ed. M. M. Novak (World Scientific, 1998), pp. 351-352.
22. K. Falconer, Fractal Geometry - Mathematical Foundations and Applications (John Wiley, 1990).
23. 20. Y. Liu, P. Cizeau, P. Gopikrishnan, M. Meyer, C.-K. Peng and H. E. Stanley, Volatility Studies of the S&P 500 Index, Preprint (1998); P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng and H. E. Stanley, "Volatility Distribution in the S&P 500 Stock Index Physica, A245, 441-445 (1997).
24. Y. Liu, P. Cizeau, P. Gopikrishnan, M. Meyer, C.-K. Peng and H. E. Stanley, Volatility Studies of the S&P 500 Index, Preprint (1998); P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng and H. E. Stanley, "Volatility Distribution in the S&P 500 Stock Index Physica, A245, 441-445 (1997).
25. Ch. Canus, J. Lévy Véhel and C. Tricot, "Continuous Large Deviation Multifractal Spectrum: Definitions and Estimation," in Fractals and Beyond - Complexities in the Sciences, ed. M. M. Novak (World Scientific, 1998), pp. 117-128.
26. J. Lévy Véhel and R. Vojak, "Multifractal Analysis of Choquet Capacities: Preliminary Results," in Advances in Applied Mathematics 20(1), 1-43 (1998).
27. J. Lévy Véhel, "Numerical Computation of the Large Deviation Multifractal Spectrum," in CFIC, Rome (1996).
28. 24. J. Lévy Véhel and R. H. Riedi, "Fractional Brownian Motion and Data Traffic Modeling: The Other End of the Spectrum," in Fractals in Engineering, eds. J. Lévy Véhel, E. Lutton and C. Tricot (Springer Verlag, 1997); R. H. Riedi and J. Lévy Véhel, TCP Traffic is Multifractal: A Numerical Study, INRIA Research Report, No. 3129 (1997).
29. J. Lévy Véhel and R. H. Riedi, "Fractional Brownian Motion and Data Traffic Modeling: The Other End of the Spectrum," in Fractals in Engineering, eds. J. Lévy Véhel, E. Lutton and C. Tricot (Springer Verlag, 1997); R. H. Riedi and J. Lévy Véhel, TCP Traffic is Multifractal: A Numerical Study, INRIA Research Report, No. 3129 (1997).
30. Heart Failure Database (Beth Israel Deaconess Medical Center, Boston, MA).