Biorthogonal multiwavelets on [-1, 1]

Applied and Computational Harmonic Analysis

Volumn 7, Issue 1, 1999, Pages 34-53

  Hardin, Douglas P ^a   Marasovich, Jeffrey A ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002016381     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1999.0261     Document Type: Article

References (17)

1. A. Aldroubi and J. McGowan, Oblique and biorthogonal multi-wavelet bases with fast-filtering algorithms, in "Wavelet Applications in Signal and Image Processing" (A. Laine and M. Unser, Eds.), SPIE - Mathematical Imaging, Vol. 2569, pp. 15-25, SPIE - Int. Soc. Opt. Eng., Bellingham, WA, 1995.
2. M. F. Barnsley, Fractal functions and interpolations, Constr. Approx. 2 (1986), 303-329.
3. A. Cohen, I. Daubechies, and J. Feauveau, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math. 41 (1989), 909-996.
4. W. Dahmen and C. A. Micchelli, Biorthogonal wavelet expansions, Constr. Approx. 13 (1997), 293-328.
5. T. Dinsenbacher and D. P. Hardin, Nonhomogeneous refinement equations, in "Wavelets, Multiwavelets and Their Applications" (Aldroubi and Lin, Eds.), AMS Contemporary Mathematics Series, Vol. 216, pp. 117-128, Amer. Math. Soc., Providence, RI, 1997.
6. G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Intertwining multiresolution analyses and the construction of piecewise polynomial wavelets, SIAM J. Math. Anal. 27 (1996), 1791-1815.
7. G. C. Donovan, J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 27 (1996), 1158-1192.
8. J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78 (1994), 373-401.
9. D. P. Hardin, B. Kessler, and P. R. Massopust, Multiresolution analyses and fractal functions, J. Approx. Theory 71 (1992), 104-120.
10. W. Lawton, S. Lee, and Z. Shen, An algorithm for matrix extension and wavelet construction, Math. Comp. 65 (1996), 723-737.
11. J. Marasovich, "Biorthogonal Multiwavelets," Dissertation, Vanderbilt University, Nashville, TN, 1996.
12. Y. Saad, "Iterative Methods for Sparse Linear Systems," PWS, Boston, 1996.
13. G. Strang and V. Strela, Short wavelets and matrix dilation equations, IEEE Trans. Signal Process. 43 (1995), 108-115.
14. P. P. Vaidyanathan, "Multirate Systems and Filter Banks," Prentice Hall, Englewood Cliffs, NJ, 1993.
15. P. P. Vaidyanathan and T. Chen, Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals, IEEE Trans. Signal Process. 43 (1995), 1090-1102.
16. P. P. Vaidyanathan and T. Chen, Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations and biorthogonal lapped transforms, IEEE Trans. Signal Process. 43 (1995), 1103-1115.
17. M. Vetterli and C. Herley, Wavelets and filter banks: Theory and design, IEEE Trans. Signal Process. 40 (1992), 2207-2232.