Multiscale denoising of self-similar processes

Journal of Geophysical Research Atmospheres

Volumn 105, Issue D22, 2000, Pages 27049-27058

  Vidakovic, Brani D ^a   Katul, Gabriel G ^b   Albertson, John D ^c  

^a Georgia Institute of Technology   (United States)

^b DUKE UNIVERSITY   (United States)

^c UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOPHYSICAL METHOD;

EID: 0034494850     PISSN: 01480227     EISSN: None     Source Type: Journal    
DOI: 10.1029/2000JD900479     Document Type: Article

References (36)

1. Berliner, M., C. Wikle, and R. Milliff, Multiresolution wavelet analyses in hierarchical Bayesian turbulence models, in Bayesian Inference in Wavelet Based Models, edited by P. Müller and B. Vidakovic, Springer-Verlag, New York, Lecture Notes in Statistics, 141, 341-349, 1999.
2. Bras, R.L. and I. Rodríguez-Iturbe, Random Functions and Hydrology, 559 pp., Dover, Mineola, N.Y., 1993.
3. Farge, M., Wavelet transforms and their applications to turbulence, Annu. Rev. Fluid Mech., 24, 395-457, 1992.
4. Farge, M., E. Goirand, Y. Meyer, F. Pascal, and M. V. Wickerhauser, Improved predictability of two-dimensional turbulent flows using wavelet packet compression, Fluid Dyn. Res., 10, 229-250, 1992.
5. Flandrin, P., Timescale analyses and self-similar stochastic processes, in Wavelets and Their Applications, edited by J. S. Byrnes et al., NATO ASI Ser., 442, 121-142, 1992.
6. Frisch, U., Turbulence, Cambridge Univ. Press, 296 pp., 1995.
7. Gupta, V. K. and E. Waymire, Statistical self-similarity in river networks parametrized by elevation, Water Resour. Res., 25, 463-476, 1989.
8. Gupta, V. K. and E. Waymire, Multiscale properties of spatial rainfall and river flow distributions, J. Geophys. Res., 95, 1999-2009, 1990.
9. Hudgins, L., C. Friehe, and M. Mayer, Wavelet Transforms and Atmospheric Turbulence, Phys. Rev. Lett., 71, 3279-3282, 1993.
10. Katul, G. and J. Albertson, Low dimensional turbulent transport mechanics near the forest atmosphere interface, in Bayesian Inference in Wavelet Based Models, edited by P. Müller and B. Vidakovic, Springer-Verlag, New York, Lecture Notes in Statistics, 141, 361-380, 1999.
11. Katul, G., P. Finkelstein, J. Clarke, and T. Ellstad, An investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars, J. Appl. Meteorol., 35, 1835-1845, 1996.
12. Katul, G., C. Hsieh, and J. Sigmon, Energy-inertial scale interaction for temperature and velocity in the unstable surface layer, Boundary Layer Meteorol., 82, 49-80, 1997a.
13. Katul, G., C. Hsieh, G. Kuhn, D. Ellsworth, and D. Nie, The turbulent eddy motion at the forest atmosphere interface, J. Geophys. Res., 102, 13409-13421, 1997b.
14. Katul, G. and B. Vidakovic, Identification of low-dimensional energy containing/flux transporting eddy motion in the atmospheric surface layer using wavelet thresholding methods, J. Atmos. Sci., 54, 91-103, 1998.
15. Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Ross. Akad. Nauk., 30, 301-305, 1941.
16. Krim, H. and J-C. Pesquet, Multiresolution analysis of a class of nonstationary processes, IEEE Trans. Inf. Theory, 4, 1010-1020, 1995.
17. Kumar, P. and E. Foufoula-Georgiou, A multicomponent decomposition of spatial rainfall fields, 2, Self-similarity in fluctuations, Water Resour. Res., 29, 2533-2544, 1993.
18. Kumar, P. and E. Foufoula-Georgiou, Wavelet analysis in geophysics: An introduction, in Wavelets in Geophysics, edited by E. Foufoula-Georgiou and P. Kumar, pp. 1-43, Academic Press, San Diego, California, 1994.
19. Leporini, D., J-C. Pesquet, and H. Krim, Bayesian approach to best basis selection, in Bayesian Inference in Wavelet Based Models, edited by P. Müller and B. Vidakovic, Springer-Verlag, New York, Lecture Notes in Statistics, 141, 155-172, 1999.
20. Lovejoy, S., Area-perimeter relation for rain and cloud areas, Science, 216, 185, 1982.
21. Mallat, S., A theory for multiresolution signal decomposition: The wavelet representation, IEEE Trans. Patt. Anal. Mach. Intel., 11, 674-693, 1989.
22. Monin, A. and A. Yaglom, Statistical Fluid Mechanics, vol. 2, 879 pp., MIT Press, Cambridge, Ma, 1975.
23. Ray, J., D. Stedman, and G. Wendel, Fast chemiluminescent method for measurement of ambient ozone, Anal. Chem., 58, 598-600, 1986.
24. Robert, C., The Bayesian Choice. Springer-Verlag, New York, 1995.
25. Saxena K. and K. Alam, Estimation of the non-centrality parameter of a chi-squared distribution, Ann. Statist., 10, 1012-1016, 1982.
26. Simoncelli, E. and E. Adelson, Noise Removal via Bayesian Wavelet Coring, in Proceedings of Third International Conference on Image Processing, IEEE Signal Processing Society, Lausanne, Switzerland, 1996.
27. Taqqu, M. Random processes with long range dependence and high variability, J. Geophys. Res., 92, 9683-9686, 1987.
28. Vannucci, M. and F. Corradi, Modeling dependence in the wavelet domain, in Bayesian Inference in Wavelet Based Models, edited by P. Müller and B. Vidakovic, Springer-Verlag, New York, Lecture Notes in Statistics, 141, 173-186, 1999.
29. Vattay, G. and A. Harnos, Scaling behavior in daily air humidity fluctuations, Phys. Rev. Lett., 73, 768, 1994.
30. Veitch, D. and P. Abry, A wavelet based joint estimator of the parameters of long-range dependence, IEEE Trans. Inf. Theor., 45, 878-897, 1999.
31. Vergassola, M. and U. Frisch, Wavelet transforms of self-similar processes, Phys. D, 54, 58-64, 1991.
32. Walter, G., Wavelets and Other Orthogonal Systems With Applications, 272 pp., CRC Press, Boca Raton, Fla., 1994.
33. Wickerhauser, M., M. Farge, E. Goirand, E. Wesfreid, and E. Cubillo, Efficiency comparison of wavelet packet and adapted local cosine bases for compression of a two-dimensional turbulent flow, in Wavelets: Theory, Algorithms, and Applications, edited by C. Chui, L. Montefusco, and L. Puccio, Academic Press, 509-531, 1994.
34. Wikle, C., M. Berliner, and N. Cressie, Hierarchical Bayesian space-time models. J. Environ. Ecol. Statist., 5, 117-154, 1998.
35. Wornell, G. W., Signal Processing With Fractals: A Wavelet Based Approach, 177 pp., Prentice Hall, Englewood Cliffs, N.J., 1996.
36. Zubair, L., K. Sreenivasan, and M. V. Wickerhauser, Compression of turbulent data and images using wavelet packets, Yale Univ., New Haven, Conn., 1990.