Compactly supported tight affine frames with integer dilations and maximum vanishing moments

Advances in Computational Mathematics

Volumn 18, Issue 2-4, 2003, Pages 159-187

  Chui, Charles K ^a,b   He, Wenjie ^a   Stöckler, Joachim ^c   Sun, Qiyu ^d  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b STANFORD UNIVERSITY   (United States)

^c TU DORTMUND UNIVERSITY   (Germany)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Compactly supported; Integer dilations; Tight affine frame; Vanishing moments

Indexed keywords

EID: 0037212665     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021318804341     Document Type: Article

References (30)

1. p, J. Fourier Anal. Appl. 7 (2001) 1-21.
2. J.J. Benedetto and S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal. 5 (1998) 389-427.
3. C.K. Chui, An Introduction to Wavelets (Academic Press, Boston, 1992).
4. C.K. Chui and W. He, Compactly supported tight frames associated with refinable functions, Appl. Comput. Harmon. Anal. 8 (2000) 293-319.
5. C.K. Chui, W. He and J. Stöckler, Compactly supported tight and sibling frames with maximal vanishing moments, Appl. Comput. Harmon. Anal., to appear.
6. C.K. Chui and X. Shi, Bessel sequences and affine frames, Appl. Comput. Harmon. Anal. 1 (1993) 29-49.
7. C.K. Chui and X.L. Shi, Orthonormal wavelets and tight frames with arbitrary real dilations, Appl. Comput. Harmon. Anal. 9 (2000) 243-264.
8. A. Cohen and Q. Sun, An arithmetic characterization of the conjugate quadrature filters associated to orthonormal wavelet bases, SIAM J. Math. Anal. 24 (1993) 1355-1360.
9. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Conference Series in Applied Mathematics, Vol. 61 (SIAM, Philadelphia, PA, 1992).
10. I. Daubechies and B. Han, Pair of dual wavelet frames from any two refinable functions, Preprint (2000).
11. I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal., to appear.
12. d), J. Funct. Anal. 119 (1994) 37-78.
13. I. Guskov, W. Sweldens and P. Schröder, Multiresolution signal processing for meshes, in: Computer Graphics Proceedings (SIGGRAPH'99), 1999, pp. 325-334.
14. B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal. 4 (1997) 380-413.
15. B. Han and Q. Mu, Multiwavelet frames from refinable function vectors, in this issue.
16. D. Hardin, T. Hogan and Q. Sun, The matrix-valued Riesz lemma and local orthonormal bases in shift-invariant spaces, in this issue.
17. E. Hernandez and G. Weiss, A First Course on Wavelets (CRC Press, Boca Raton, FL, 1996).
18. R.-Q. Jia and J.Z. Wang, Stability and linear independence associated with wavelet decompositions, Proc. Amer. Math. Soc. 117 (1993) 1115-1124.
19. W.M. Lawton, Tight frames of compactly supported affine wavelets, J. Math. Phys. 31 (1990) 1898-1901.
20. W. Lawton, S.L. Lee and Z. Shen, An algorithm for matrix extension and wavelet construction, Math. Comp. 65 (1996) 723-737.
21. W. Lawton, S.L. Lee and Z. Shen, Stability and orthonormality of multivariable refinable functions, SIAM J. Math. Anal. 28 (1997) 999-1014.
22. P.G. Lemarie, Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions, Rev. Mat. Iberoamericana 10 (1994) 283-347.
23. L.-M. Reissell, Wavelet multiresolution representation of curves and surfaces, CVGIP: Graphical Models Image Process. 58 (1996) 198-217.
24. W.C. Rheinboldt and J.S. Vandergraft, A simple approach to the Perron Frobenius theory for positive operators on general partially-order finite-dimensional linear spaces, Math. Comp. 27 (1973) 139-145.
25. d): The analysis of the analysis operator, J. Funct. Anal. 148 (2) (1997) 408-447.
26. P. Schröder, Wavelets in computer graphics, Proc. IEEE 84 (1996) 615-625.
27. E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for Computer Graphics: Theory and Applications (Morgan Kaufmann, San Francisco, CA, 1996).
28. Q. Sun, An algorithm for the construction of symmetric and anti-symmetric M-band wavelets, Proc. SPIE 4119 (2000) 384-394.
29. Q. Sun, N. Bi and D. Huang, An Introduction to Multiband Wavelets (Zhejiang Univ. Press, Hangzhou, China, 2001).
30. D.X. Zhou, Stability of refinable functions, multiresolution analysis and Haar bases, SIAM J. Math. Anal. 27 (1996) 891-904.