A Construction of C1-Wavelets on the Two-Dimensional Sphere

Applied and Computational Harmonic Analysis

Volumn 10, Issue 1, 2001, Pages 1-26

  Weinreich, Ilona ^a  

^a UNIVERSITY OF APPLIED SCIENCES KOBLENZ   (Germany)

Author keywords

Multiresolution analysis; wavelets; exponential splines; tensor product splines; wavelets on surfaces

Indexed keywords

EID: 0346510236     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0330     Document Type: Article

References (27)

1. Andersson L., Hall N., Jawerth B., Peters G. Wavelets on closed subsets of the real line. Schumaker L. L., Webb G. Topics in the Theory and Applications of Wavelets. 1994;1-61 Academic Press, Boston.
2. Chui C. K., Quak E. Wavelets on a bounded interval. Braess D., Schumaker L. L. Numerical Methods of Approximation Theory. 1992;1-24 Birkhäuser, Basel.
3. Cohen A., Daubechies I., Feauveau J. Bi-orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45:1992;485-560.
4. Carnicer J. M., Dahmen W., Peña J. M. Local decomposition of refinable spaces. Appl. Comput. Harmon. Anal. 3:1996;127-153.
5. Cohen A., Daubechies I., Vial P. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1:1993;54-81.
6. A. Cohen, L.-M. Echeverry, and, Q. Sun, Finite element wavelets, Preprint University Pierre et Marie Curie, Paris, 2000.
7. Dahmen W. Stability of multiscale transformations. J. Fourier Anal. Appl. 4:1996;341-362.
8. Dahmen W. Multiscale analysis, approximation, and interpolation spaces. Chui C. K., Schumaker L. L. Approximation Theory VIII. 1995;47-88 World Scientific, Singapore.
9. de Boor C., DeVore R. A., Ron A. On the construction of multivariate (pre)wavelets. Constr. Approx. 9:1993;123-166.
10. 3. Numer. Funct. Anal. Optim. 16:1995;19-41.
11. Dahmen W., Kunoth A., Urban K. Biorthogonal spline wavelets on the interval - stability and moment conditions. Appl. Comput. Harmon. Anal. 6:1999;132-196.
12. Dahmen W., Micchelli C. A. On multivariate E-splines. Adv. in Math. 76:1989;33-93.
13. Dahmen W., Micchelli C. A. Banded matrices with banded inverses, II: Locally finite decomposition of spline spaces. Constr. Approx. 9:1993;263-281.
14. Dahmen W., Schneider R. Wavelets on manifolds I: construction and domain decomposition. SIAM J. Math. Anal. 31:1999;184-230.
15. Freeden W., Schreiner M. Orthogonal and nonorthogonal multiresolution analysis, scale discrete and exact fully discrete wavelet transform on the sphere. Constr. Approx. 14:1998;493-515.
16. Gmelig Meyling R. H. J., Pfluger P. R. B-spline approximation of a closed surface. IMA J. Numer. Anal. 7:1987;73-96.
17. Göttelmann J. Locally supported wavelets on manifolds with applications to the 2D sphere. Appl. Comput. Harmon. Anal. 7:1999;1-33.
18. Lyche T., Schumaker L. L. L-spline wavelets. Chui C. K., Montefusco L., Puccio L. Wavelets: Theory, Algorithms, and Applications. 1994;197-212 Academic Press, San Diego.
19. Potts D., Tasche M. Interpolatory wavelets on the sphere. Chui C. K., Schumaker L. L. Approximation Theory VIII. 1995;335-342 World Scientific, Singapore.
20. Potts D., Steidl G., Tasche M. Kernels of spherical harmonics and spherical frames. Fontanella F., Jetter K., Laurent P.-J. Advanced Topics in Multivariate Approximation. 1996;World Scientific, Singapore.
21. Ron A. Exponential box splines. Constr. Approx. 4:1988;357-378.
22. Schroeder P., Sweldens W. Spherical wavelets: Efficiently representing functions on the sphere. Computer Graphics Proceedings (SIGGRAPH 95). 1995;. p. 161-172.
23. Sweldens W. The lifting scheme: A custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 3:1996;186-200.
24. Sweldens W. The lifting scheme: A construction of second generation wavelets. SIAM J. Math Anal. 2:1997;511-546.
25. Schumaker L. L., Traas C. Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines. Numer. Math. 60:1991;133-144.
26. Weinreich I. Biorthogonale Wavelets auf der Sphäre. 1997;Shaker, Aachen.
27. Windheuser U. Sphärische Wavelets: Theorie und Anwendungen in der Physikalischen Geodäsie. 1995;Univ. Kaiserslautern.