Multiscale representation and analysis of spherical data by spherical wavelets

SIAM Journal of Scientific Computing

Volumn 21, Issue 3, 1999, Pages 924-953

  Li, Ta Hsin ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CLIMATOLOGY; DATA COMPRESSION; FUNCTION EVALUATION; POISSON DISTRIBUTION; REGRESSION ANALYSIS; TIME SERIES ANALYSIS;

MULTIRESOLUTION METHOD; OBJECTIVE ANALYSIS; POISSON KERNEL; SPHERICAL HARMONICS;

WAVELET TRANSFORMS;

EID: 0033294725     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598341463     Document Type: Article

References (36)

1. M. AKAY, ED., Time Frequency and Wavelets m Biomedical Signal Processing, IEEE Press, Piscataway, NJ, 1998.
2. G. B. ARFKEN AND H. J. WEBER, Mathematical Methods for Physicists, 4th ed., Academic Press, San Diego, 1995.
3. E. J. BARRON, D. HARTMANN, D. SCHIMEL, AND M. SCHOEBERL, Earth Observing System: Science Contributions to National Goals and Interests, Tech. Report, Earth System Science Center, Pennsylvania State University, University Park, PA, 1995.
4. W. BOURKE, Spectral methods in global climate and weather prediction models, in Physically-Based Modeling and Simulation of Climate and Climate Change, Part I, M. E. Schlesinger, ed., Kluwer Academic Press, New York. 1988, pp. 169-220.
5. M. D. BUHMANN AND C. A. MICCHELLI, Spline prewavelets for non-uniform knots Numer. Math., 61 (1992), pp. 445-474.
6. C. K. CHUI, An Introduction to Wavelets, Academic Press, San Diego, 1992.
7. R. DALEY, Atmospheric Data Analysis, Cambridge University Press, Cambridge, UK, 1991.
8. I. DAUBECHIES, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math. 61, SIAM, Philadelphia, PA, 1992.
9. R. A. DEVORE, B. JAWERTH, AND B. L. LUCIER, Image compression through wavelet transform coding, IEEE Trans. Inform. Theory, 38 (1992), pp. 719-746.
10. D. L. DONOHO, De-noising by soft-thresholding, IEEE Trans. Inform. Theory, 41 (1995), pp. 613-627.
11. D. L. DONOHO AND I. M. JOHNSTONE, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 18 (1994), pp. 425-455.
12. W. FREEDEN AND U. WINDHEUSER, Spherical wavelet transform and its discretization, Adv. Comput. Math., 5 (1996), pp. 51-94.
13. W. FREEDEN AND U. WINDHEUSER, Combined spherical harmonics and wavelet expansion - A future concept in earth's gravitational determination, Appl. Comput. Harmon. Anal., 4 (1997), pp. 1-37.
14. T. J. HASTIE AND R. J. TIBSHIRANI, Generalized Additive Models, Chapman & Hall, London, 1990.
15. P. D. JONES, S. C. B. RAPER, B. S. G. CHERRY, C. M. GOODESS, T. M. L. WIGLEY, B. SANTER, P. M. KELLY, R. S. BRADLEY, AND H. F. DIAZ, An Updated Global Grid Point Surface Temperature Anomaly Data Set: 1851-1988, Environmental Sciences Division Publication No. 3520, U. S. Department of Energy, Washington, DC, 1991.
16. K.-Y. KIM AND G. R. NORTH, EOF analysis of surface temperature field in a stochastic climate model, J. Climate, 6 (1993), pp. 1681-1690.
17. S. S. LEROY, Measurement of geopotential heights by GPS radio occultation. J. Geophysical Research, 102 (1997), pp. 6971-6986.
18. T. H. LI, Multiscale Representation of Spherical Data by Spherical Wavelets, Tech. Report 356, Department of Statistics and Applied Probability, University of California, Santa Barbara, 1998.
19. T. H. LI, Multiscale Wavelet Analysis of Spherical Data: Design and Estimation, Tech. Report 358, Department of Statistics and Applied Probability, University of California, Santa Barbara, 1999.
20. T. H. LI AND M. J. HINICH. A Filter Bank Approach for Modeling and Forecasting Seasonal Patterns, Tech. Report 355, Department of Statistics and Applied Probability, University of California, Santa Barbara, 1998.
21. T. H. LI, G. R. NORTH, AND S. S. SHEN, Aliased power of a stochastic temperature field on a sphere, J. Geophysical Research, 102 (1997), pp. 4475-4489.
22. Z. LUO, G. WAHBA, AND D. R. JOHNSON, Spatial-temporal analysis of temperature using smoothing spline. ANOVA, J. Climate, 11 (1997), pp. 18-29.
23. S. MALLAT, A theory of multiresolution signal decomposition: The wavelet representation, IEEE Trans. Pattern Analysis and Machine Intelligence, 11 (1989), pp. 674-693.
24. S. MALLAT AND W. L. HWANG, Singularity detection and processing with wavelets. IEEE Trans. Inform. Theory, 38 (1992), pp. 617-643.
25. F. J. NARCOWICH AND J. D. WARD, Nonstationary wavelets on the m-sphere for scattered data, Appl. and Comput. Harmon. Anal., 3 (1996), pp. 324-336.
26. F. J. NARCOWICH, N. SIVAKUMAR, AND J. D. WARD, Stability results for scattered-data interpolation on Euclidean spheres, Adv. Comput. Math., 8 (1998), pp. 137-163.
27. P. SCHRÖDER AND W. SWELDENS, Spherical wavelets: Efficiently representing functions on the sphere, Computer Graphics Proceedings, SIGGRAPH95, 1995, pp. 161-172.
28. M. SCHREINER, On a new condition for strictly positive definite functions on spheres, Proc. Amer. Math. Soc., 125 (1997), pp. 531-539.
29. J. M. SHAPIRO, Embedded image, coding using zero trees of wavelet coefficients, IEEE Trans. Signal Processing, 41 (1993), pp. 3445-3462.
30. S. S. SHEN, G. R. NORTH, AND K.-Y. KIM, Spectral approach to optimal estimation of the global average temperature, J. Climate, 7 (1994), pp. 1999-2007.
31. G. STRANG AND T. NGUYEN, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1996.
32. M. VETTERLI AND J. KOVAČEVIĆ. Wavelets and Subband Coding, Prentice-Hall, Upper Saddle River, NJ, 1995.
33. K. Y. VINNIKOV, P. Y. GROISMAN, AND K. M. LUGINA, Empirical data on contemporary global climate changes (temperature and precipitation), J. Climate, 3 (1990), pp. 662-677.
34. G. WAHBA, Spline interpolation and smoothing on the sphere, SIAM J. Sci. Statist. Comput, 2 (1981), pp. 5-16; Erratum, SIAM J. Sci. Statist. Comput., 3 (1982), pp. 385-386.
35. G. WAHBA, Spline Models for Observational Data, SIAM, Philadelphia, PA, 1990.
36. W. M. WASHINGTON AND C. L. PARKINSON, An Introduction to Three-Dimensional Climate Modeling, Univ. Sci. Books, Mill Valley, CA. 1986.