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Part II: Second generation wavelets

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Book cover Wavelets in the Geosciences

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 90))

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References

  1. L. Andersson, N. Hall, B. Jawerth, and G. Peters. Wavelets on closed subsets of the real line. In [23], pages 1–61.

    Google Scholar 

  2. J. M. Carnicer, W. Dahmen, and J. M. Peña. Local decompositions of refinable spaces. Appl. Comput. Harmon. Anal., 3:127–153, 1996.

    Google Scholar 

  3. C. Chui and E. Quak. Wavelets on a bounded interval. In D. Braess and L. L. Schumaker, editors, Numerical Methods of Approximation Theory, pages 1–24. Birkhäuser-Verlag, Basel, 1992.

    Google Scholar 

  4. C. K. Chui, L. Montefusco, and L. Puccio, editors. Conference on Wavelets: Theory Algorithms, and Applications. Academic Press, San Diego, CA, 1994.

    Google Scholar 

  5. A. Cohen, I. Daubechies, and J. Feauveau. Bi-orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 45:485–560, 1992.

    Google Scholar 

  6. A. Cohen, I. Daubechies, and P. Vial. Multiresolution analysis, wavelets and fast algorithms on an interval. Appl. Comput. Harmon. Anal., 1(1):54–81, 1993.

    Google Scholar 

  7. W. Dahmen. Stability of multiscale transformations. J. Fourier Anal. Appl., 2(4):341–361, 1996.

    Google Scholar 

  8. W. Dahmen, S. Prössdorf, and R. Schneider. Multiscale methods for pseudo-differential equations on smooth manifolds. In [4], pages 385–424. 1994.

    Google Scholar 

  9. I. Daubechies. Ten Lectures on Wavelets. CBMS-NSF Regional Conf. Series in Appl. Math., Vol. 61. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.

    Google Scholar 

  10. G. Deslauriers and S. Dubuc. Interpolation dyadique. In Fractals, dimensions non entières et applications, pages 44–55. Masson, Paris, 1987.

    Google Scholar 

  11. G. Deslauriers and S. Dubuc. Symmetric iterative interpolation processes. Constr. Approx., 5(1):49–68, 1989.

    Google Scholar 

  12. D. L. Donoho. Smooth wavelet decompositions with blocky coefficient kernels. In [23], pages 259–308.

    Google Scholar 

  13. D. L. Donoho. Interpolating wavelet transforms. Preprint, Department of Statistics, Stanford University, 1992.

    Google Scholar 

  14. D. L. Donoho and I. M. Johnstone. Ideal spatial adaptation via wavelet shrinkage. Biometrika, to appear, 1994.

    Google Scholar 

  15. D. L. Donoho and I. M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. 1995.

    Google Scholar 

  16. N. Dyn, D. Levin, and J. Gregory. A 4-point interpolatory subdivision scheme for curve design. Comput. Aided Geom. Des., 4:257–268, 1987.

    Google Scholar 

  17. M. Girardi and W. Sweldens. A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure spaces. J. Fourier Anal. Appl., 3(4), 1997.

    Google Scholar 

  18. M. Lounsbery, T. D. DeRose, and J. Warren. Multiresolution surfaces of arbitrary topological type. ACM Trans. on Graphics, 16(1):34–73, 1997.

    Google Scholar 

  19. S. G. Mallat. Multiresolution approximations and wavelet orthonormal bases of L2(ℜ211D;). Trans. Amer. Math. Soc., 315(1):69–87, 1989.

    Google Scholar 

  20. Y. Meyer. Ondelettes et Opérateurs, I: Ondelettes, II: Opérateurs de Calderón-Zygmund, III: (with R. Coifman), Opérateurs multilinéaires. Hermann, Paris, 1990. English translation of first volume, Wavelets and Operators, is published by Cambridge University Press, 1993.

    Google Scholar 

  21. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes. Cambridge University Press, 2nd edition, 1993.

    Google Scholar 

  22. P. Schröder and W. Sweldens. Spherical wavelets: Efficiently representing functions on the sphere. Computer Graphics Proceedings, (SIGGRAPH 95), pages 161–172, 1995.

    Google Scholar 

  23. L. L. Schumaker and G. Webb, editors. Recent Advances in Wavelet Analysis. Academic Press, New York, 1993.

    Google Scholar 

  24. J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Springer Verlag, New York, 1980.

    Google Scholar 

  25. W. Sweldens. Construction and Applications of Wavelets in Numerical Analysis. PhD thesis, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, 1994.

    Google Scholar 

  26. W. Sweldens. The lifting scheme: A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal., 3(2):186–200, 1996.

    Google Scholar 

  27. W. Sweldens. The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal., 29(2):511–546, 1997.

    Google Scholar 

  28. M. Vetterli and C. Herley. Wavelets and filter banks: Theory and design. IEEE Trans. Acoust. Speech Signal Process., 40(9):2207–2232, 1992.

    Google Scholar 

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Roland Klees Roger Haagmans

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(2000). Part II: Second generation wavelets. In: Klees, R., Haagmans, R. (eds) Wavelets in the Geosciences. Lecture Notes in Earth Sciences, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0011094

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  • DOI: https://doi.org/10.1007/BFb0011094

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  • Print ISBN: 978-3-540-66951-7

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