An algebraic construction of k-balanced multiwavelets via the lifting scheme

Numerical Algorithms

Volumn 23, Issue 4, 2000, Pages 329-356

  Bacchelli, S ^a   Cotronei, M ^b   Lazzaro, D ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF MESSINA   (Italy)

^c UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Balanced multiwavelets; Biorthogonal filters; Block recursive matrices; Lifting scheme

Indexed keywords

EID: 0034377268     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019120621646     Document Type: Article

References (26)

1. S.Bacchelli, Block Toeplitz and Hurwitz matrices: a recursive approach, Adv. in Appl. Math. 23 (1999) 199-210.
2. S. Bacchelli, M. Cotronei and D. Lazzaro, A recursive approach to the construction of k-balanced biorthogonal multifilters, in: Proc. of 5th Internat. Conf. on Mathematical Methods for Curves and Surfaces (1999) to appear.
3. S. Bacchelli and D. Lazzaro, Some practical applications of block recursive matrices, to appear in Internat. J. Comput. Math. Appl. (1999).
4. M. Barnabei and L. Montefusco, Recursive properties of Toeplitz and Hurwitz matrices, Linear Algebra Appl. 274 (1998) 367-388.
5. C.K. Chui, An Introduction to Wavelets (Academic Press, New York, 1992).
6. C.K. Chui and J. Lian, A study of orthonormal multi-wavelets, Appl. Numer. Math. 20 (1996) 273-298.
7. M. Cotronei, D. Lazzaro, L.B. Montefusco and L. Puccio, Image compression through embedded multiwavelet transform coding, IEEE Trans. Image Process. (1999) to appear.
8. M. Cotronei, L.B. Montefusco and L. Puccio, Multiwavelet analysis and signal processing, IEEE Trans. Circuits Systems II: Analog Digital Signal Process. 45 (1998) 970-987.
9. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, PA, 1992).
10. I. Daubechies and W. Sweldens, Factoring wavelet transform into lifting steps, Technical Report, Bell Labs (1996).
11. J.S. Geronimo, D.P. Hardin and P.R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78(3) (1994) 373-401.
12. S.S. Goh, Q. Jiang and T. Xia, Construction of biorthogonal multiwavelets using the lifting scheme, preprint.
13. T.N.T. Goodman and S.L. Lee, Wavelets of multiplicity r, Trans. Amer. Math. Soc. 342(1) (1994) 307-324.
14. D.P. Hardin and D.W. Roach, Multiwavelet prefilters I: Orthogonal prefilters preserving approximation order p ≤ 2, IEEE Trans. Circuits Systems II: Analog Digital Signal Process. 45 (1998) 1106-1112.
15. Q. Jiang, On the construction of biorthogonal multiwavelet bases, preprint (1997).
16. D. Lazzaro, Biorthogonal M-band filter construction using the lifting scheme, Numer. Algorithms 22 (1999) 53-72.
17. J. Lebrun and M. Vetterli, Balanced multiwavelets: Theory and design, IEEE Trans. Signal Process. 46 (1998).
18. J. Lebrun and M. Vetterli, High order balanced multiwavelets: theory, factorization and design, preprint.
19. C. Micchelli and T. Sauer, Regularity of multiwavelets, Adv. Comput. Math. 7(4) (1997) 455-545.
20. G. Plonka, Approximation order provided by refinable function vectors, Constr. Approx. (1995).
21. G. Plonka and V. Strela, Construction of multiscaling functions with approximation and symmetry, SIAM J. Math. Anal. (1995).
22. I. Selesnick, Multiwavelet bases with extra approximation properties, IEEE Trans. Signal Process. 46 (1998) 2898-2908.
23. G. Strang and V. Strela, Short wavelets and matrix dilation equations, IEEE Trans. Signal Process. 43 (1995) 108-115.
24. W. Sweldens, The lifting scheme: a custom-design construction of biorthogonal wavelets, Appl. Comput. Harmon. Anal. 3 (1996) 186-200.
25. P.P. Vaidyanathan, Multirate Systems and Filter Banks (Prentice-Hall, Englewood Cliffs, NJ, 1995).
26. X.G. Xia, J.S. Geronimo, D.P. Hardin and B.W. Suter, Design of prefilters for discrete multiwavelet transforms, IEEE Trans. Signal Process. 44 (1996) 25-35.