Symmetric-Antisymmetric Orthonormal Multiwavelets and Related Scalar Wavelets

Applied and Computational Harmonic Analysis

Volumn 8, Issue 3, 2000, Pages 258-279

  Shen, L ^a   Tan, H H ^a   Tham, J Y ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001139391     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1999.0288     Document Type: Article

References (24)

1. Chui C. K., Lian J. A study on orthonormal multiwavelets. Appl. Numer. Math. 20:1996;273-298.
2. Cohen A., Daubechies I., Plonka G. Regularity of refinable function vectors. J. Fourier Anal. Appl. 3:1997;295-324.
3. Dahmen W., Micchelli C. A. Biorthogonal wavelet expansions. Constr. Approx. 13:1997;293-328.
4. Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Reg. Conf. Series on Appl. Math. 61:1992;SIAM, Philadelphia.
5. Daubechies I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41:1988;909-996.
6. Donovan G., Geronimo J. S., Hardin D. P., Massopust P. R. Construction of orthogonal wavelets using fractal interpolation functions. SIAM J. Math. Anal. 27:1996;1158-1192.
7. Geronimo J. S., Hardin D. P., Massopust P. R. Fractal functions and wavelet expansions based on several scaling functions. J. Approx. Theory. 78:1994;373-401.
8. Goodman T. N. T., Lee S. L., Tang W. S. Wavelet in wandering subspaces. Trans. Amer. Math. Soc. 338:1993;639-654.
9. Goodman T. N. T., Lee S. L. Wavelets of multiplicity r. Trans. Amer. Math. Soc. 342:1994;307-324.
10. Heil C., Strang G., Strela V. Approximation by translates of refinable functions. Numer. Math. 73:1996;75-94.
11. Jiang Q. On the regularity of matrix refinable functions. SIAM J. Math. Anal. 29:1998;1157-1176.
12. Jiang Q. Orthogonal multiwavelets with optimum time-frequency resolution. IEEE Trans. Signal Process. 46:1997;830-844.
13. Jiang Q., Shen Z. On existence and weak stability of matrix refinable functions. Constr. Approx. 15:1999;337-353.
14. Lawton W., Lee S. L., Shen Z. An algorithm for matrix extension and wavelet construction. Math. Comput. 65:1996;723-737.
15. Micchelli C. A., Sauer T. Regularity of multiwavelets. Adv. Comput. Math. 7:1997;455-545.
16. Plonka G. Approximation order provided by refinable function vectors. Constr. Approx. 13:1997;221-244.
17. Shen Z. Refinable function vectors. SIAM J. Math. Anal. 29:1998;234-249.
18. Strang G., Strela V. Short wavelets and matrix dilation equations. IEEE Trans. Signal Process. 43:1995;108-115.
19. Strela V., Heller P. N., Strang G., Topiwala P., Heil C. The application of multiwavelet filter banks to image processing. IEEE Trans. Image Process. 8:1999;548-563.
20. Strang G., Nguyen T. Wavelets and Filter Banks. 1996;Wellesley.
21. Tham J. Y., Shen L., Lee S. L., Tan H. H. Good multifilter properties: a new tool for understanding multiwavelets. Proceedings for International Conference on Imaging Science, Systems and Technology (CISST98), Las Vegas. 1988;. p. 52-59.
22. Vaidyanathan P. P. Multirate Systems and Filter Banks. 1993;Prentice-Hall, Englewod Cliffs.
23. Villemoes L. F. Energy moments in time and frequency for two-scale difference equation solutions and wavelets. SIAM J. Math. Anal. 23:1992;1519-1543.
24. Xia X. G., Geronimo J. S., Hardin D. P., Suter B. W. Design of prefilters for discrete multiwavelet transform. IEEE Trans. Signal Process. 44:1996;25-35.