Wavelet entropy of stochastic processes

Physica A: Statistical Mechanics and its Applications

Volumn 379, Issue 2, 2007, Pages 503-512

  Zunino, L ^a,b,c   Perez D G ^d   Garavaglia, M ^a,c   Rosso, O A ^e  

^a CENTRO DE INVESTIGACIONES OPTICAS   (Argentina)

^b UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^c FACULTAD DE CIENCIAS EXACTAS   (Argentina)

^d PONTIFICIA UNIVERSIDAD CATÓLICA DE VALPARAÍSO   (Chile)

^e INSTITUTO DE CÁLCULO   (Argentina)

Author keywords

parameter; Fractional Brownian motion; Fractional Gaussian noise; Wavelet analysis; Wavelet entropy

Indexed keywords

ELECTROENCEPHALOGRAPHY; FREQUENCY DOMAIN ANALYSIS; FUNCTION EVALUATION; GAUSSIAN NOISE (ELECTRONIC); TIME DOMAIN ANALYSIS; WAVELET ANALYSIS;

Α-PARAMETER; FRACTIONAL BROWNIAN MOTION; FRACTIONAL GAUSSIAN NOISE; WAVELET ENTROPY;

BROWNIAN MOVEMENT;

EID: 34247543875     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.12.057     Document Type: Article

References (36)

1. Daubechies I. Ten Lectures on Wavelets (1992), SIAM, Philadelphia
2. Mallat S. A Wavelet Tour of Signal Processing. second ed. (1999), Academic Press, New York
3. Blanco S., Figliola A., Quiroga R.Q., Rosso O.A., and Serrano E. Time-frequency analysis of electroencephalogram series, III. Wavelet packets and information cost function. Phys. Rev. E 57 (1998) 932-940
4. Rosso O.A., Blanco S., Yordanova J., Kolev V., Figliola A., Schürmann M., and Başar E. Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J. Neurosci. Method 105 (2001) 65-75
5. Rosso O.A., and Mairal M.L. Characterization of time dynamical evolution of electroencephalographic epileptic records. Physica A 312 3-4 (2002) 469-504
6. Rosso O.A., Martín M.T., and Plastino A. Brain electrical activity analysis using wavelet based informational tools. Physica A 313 (2002) 587-608
7. Hasegawa H. Stochastic resonance of ensemble neurons for transient spike trains: wavelet analysis. Phys. Rev. E 66 2 (2002) 021902
8. Rosso O.A., Blanco S., and Rabinowicz A. Wavelet analysis of generalized tonic-clonic epileptic seizures. Signal Process. 86 (2003) 1275-1289
9. Al-Nashash H.A., Paul J.S., Ziai W.C., Hanley D.F., and Thakor N.V. Wavelet entropy for subband segmentation of EEG during injury and recovery. Ann. Biomed. Eng. 31 (2003) 653-658
10. Rosso O.A., Hyslop W., Gerlach R., Smith R.L.L., Rostas J.A.P., and Hunter M. Quantitative EEG analysis of the maturational changes associated with childhood absence epilepsy. Physica A 356 1 (2005) 184-189
11. Al-Nashash H.A., and Thakor N.V. Monitoring of global cerebral ischemia using wavelet entropy rate of change. IEEE Trans. Biomed. Eng. 52 12 (2005) 2119-2122
12. Shin H.C., Tong S., Yamashita S., Jia X., Geocadin R.G., and Thakor N.V. Quantitative EEG and effect of hypothermia on brain recovery after cardiac arrest. IEEE Trans. Biomed. Eng. 53 6 (2006) 1016-1023
13. Chiu A.W.L., Jahromi S.S., Khosravani H., Carlen P.L., and Bardakjian B.L. The effects of high-frequency oscillations in hippocampal electrical activities on the classification of epileptiform events using artificial neural networks. J. Neural Eng. 3 1 (2006) 9-20
14. Rosso O.A., Martin M.T., Figliola A., Keller K., and Plastino A. EEG analysis using wavelet-based information tools. J. Neurosci. Method 153 2 (2006) 163-182
15. Sello S. Wavelet entropy as a measure of solar cycle complexity. Astron. Astrophys. 363 (2000) 311-315
16. Sello S. Wavelet entropy and the multi-peaked structure of solar cycle maximum. New Astron. 8 (2003) 105-117
17. Korol A.M., Rasia R.J., and Rosso O.A. Alterations of thalassemic erythrocytes detected by wavelet entropy. Physica A 375 1 (2007) 257-264
18. Zunino L., Pérez D.G., Garavaglia M., and Rosso O.A. Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform. Fractals 12 2 (2004) 223-233
19. Zunino L., Pérez D.G., Garavaglia M., and Rosso O.A. Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study. Physica A 364 (2006) 79-86
20. Passoni I., Dai Pra A., Rabal H., Trivi M., and Arizaga R. Dynamic speckle processing using wavelets based entropy. Opt. Commun. 246 1-3 (2005) 219-228
21. González C.M., Larrondo H.A., and Rosso O.A. Statistical complexity measure of pseudorandom bit generators. Physica A 354 (2005) 281-300
22. Kowalski A.M., Martín M.T., Plastino A., Proto A.N., and Rosso O.A. Wavelet statistical complexity analysis of the classical limit. Phys. Lett. A 311 (2003) 180-191
23. Pérez D.G., Zunino L., Garavaglia M., and Rosso O.A. Wavelet entropy and fractional Brownian motion time series. Physica A 365 2 (2006) 282-288
24. Tavares D.M., and Lucena L.S. Entropy analysis of stochastic processes at finite resolution. Physica A 357 1 (2005) 71-78
25. Carbone A., Castelli G., and Stanley H.E. Time-dependent Hurst exponent in financial time series. Physica A 344 1-2 (2004) 267-271
26. Addison P.S., and Ndumu A.S. Engineering applications of fractional Brownian motion: self-affine and self-similar random processes. Fractals 7 2 (1999) 151-157
27. Shannon C.E. A mathematical theory of communications. Bell Syst. Technol. J. 27 (1948) 379-423 and 623-656
28. Mandelbrot B.B., and Van Ness J.W. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 4 (1968) 422-437
29. Samorodnitsky G., and Taqqu M.S. Stable non-Gaussian random processes: stochastic models with infinite variance (1994), Chapman & Hall/CRC, London, UK
30. Flandrin P. Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. Inform. Theory IT-38 2 (1992) 910-917
31. Abry P., Flandrin P., Taqqu M.S., and Veitch D. Wavelets for the analysis, estimation, and synthesis of scaling data. In: Park K., and Willinger W. (Eds). Self-similar Network Traffic and Performance Evaluation (2000), Wiley, New York
32. Boffetta G., Cencini M., Falcioni M., and Vulpiani A. Predictability: a way to characterize complexity. Phys. Reports 356 (2002) 367-474
33. Urbanowicz K., and Holyst J.A. Noise-level estimation of time series using coarse-grained entropy. Phys. Rev. E 67 (2003) 046218
34. Anghel M. On the effective dimension and dynamic complexity of earthquake faults. Chaos, Solitons & Fractals 19 2 (2004) 399-420
35. Holden H., Øksendal B., Ubøe J., and Zhang T. Stochastic Partial Differential Equations: a Modeling, White Noise Functional Approach, Probability and Its Applications (1996), Birkhäuser, Boston
36. Elliott R.J., and van der Hoek J. A general fractional white noise theory and applications to finance. Math. Finance 13 (2003) 301-330