Wavelet bases on the sphere obtained by radial projection

Journal of Fourier Analysis and Applications

Volumn 13, Issue 4, 2007, Pages 421-434

  Roşca, Daniela ^a  

^a TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Spherical multiresolution analysis; Spherical wavelets

Indexed keywords

EID: 34547512183     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-006-6014-z     Document Type: Conference Paper

References (23)

1. Antoine, J-P. and Vandergheynst, P. (1999). Wavelets on die 2-sphere: A group-theoretical approach, Appl. Comput. Harmon. Anal. 7, 262-291.
2. Antoine, J-P., Demanet, L., Jacques, L., and Vandergheynst, P. (2002). Wavelets on the sphere: Implementation and approximations, Appl. Comput. Harmon, Anal. 13, 177-200.
3. Bogdavova, I., Vandergheynst, R, Antoine, J-P., Jacques, L., and Morvidone, M. (2005). Stereographic wavelet frames on the sphere, Appl. Comput. Harmon. Anal. 26, 223-252.
4. Bonneau, G-P. (1999). Optimal triangular Haar bases for spherical data, in Visualization '99, Gross, M., Ebert, D. S., and Hamann, B., Eds., IEEE Computer Society Press, CA, 279-284.
5. Dahlke, S. and Maass, P. (1996). Continuous wavelet transforms with applications to analyzing functions on the spheres, J. Fourier Anal. Appl. 2(4), 379-396.
6. 3, Numer. Funct. Anal. Optim. 16, 19-41.
7. Floater, M. and Quak, E. (1999). Piecewise linear prewavelets on arbitrary triangulations, Numer. Math, 82, 221-252.
8. Freeden, W. and Schreiner, M. (2005). Spaceborne gravitational field determination by means of locally supported wavelets, Journal of Geodesy 79, 431-446.
9. Freeden, W. and Windheuser, U. (1997). Combined spherical harmonics and wavelet expansions-A future concept in earth's gravitational potential determination, Appl. Comput. Harmon. Anal. 4, 1-37.
10. Holschneider, M. (1996). Continuous wavelet transforms on the sphere, J. Math. Phys. 37, 4158-4165.
11. Narcowich, F. and Ward, J. ( 1996). Nonstationary wavelets on the m-sphere for scattered data, Appl. Comput. Harmon. Anal. 3, 324-336.
12. Nielson, G., Jung, I., and Sung, J. (1997). Haar wavelets over triangular domains with applications to multiresolution models for flow over a sphere, in IEEE Visualization '97, 143-150.
13. Potts, D. and Tasche, M. (1995). Interpolatory wavelets on the sphere, in Approximation Theory VIII, Chui, C. K. and Schumaker, L.L., Eds., World Scientific, Singapore, 335-342.
14. Roşca, D. (2005). Locally supported rational spline wavelets on the sphere, Math. Comput. 74, 252, 1803-1829.
15. Roşca, D. (2005). Haar wavelets on spherical triangulations, in Advances in Multiresolution for Geometric Modelling, Dodgson, N. A., Floater, M. S., and Sabin, M. A., Eds., Springer Verlag, 407-419.
16. Roşca, D. (2006). Optimal Haar wavelets on spherical triangulations, Pure Math. Appl. 16(4), 429-438.
17. Roşca, D. (2006). Piecewise constant wavelets defined on closed surfaces, J. Comput. Anal. Appl. 8(2), 121-132.
18. Roşca, D. (2007). Weighted Haar wavelets on the Sphere, Int. J. Waveletes Multiresolut. Inf. Process. 3(5), to appear.
19. 2), preprint.
20. Roşca, D. (2006). Piecewise constant wavelets on triangulations, obtained by 1-3 splitting, submitted.
21. Roşca, D. and Antoine, J-P. (2007). Locally supported orthogonal wavelets on the sphere via stereographic projection, preprint.
22. Schröder, P. and Sweldens, W. (1995). Spherical wavelets: Efficiently representing functions on the sphere, in Computer Graphics Proceedings (SIGGRAPH 1995), 161-175.
23. 1-Wavelets on the two-dimensional sphere, Appl. Comput. Harmon. Anal. 10, 1-26.