Vector-valued wavelets and vector filter banks

IEEE Transactions on Signal Processing

Volumn 44, Issue 3, 1996, Pages 508-518

  Xia, Xiang Gen ^b   Suter, Bruce W ^a,c  

^a IEEE

^b Hughes Aircraft Co   (United States)

^c AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIGITAL SIGNAL PROCESSING; IMAGE CODING; TIME DOMAIN ANALYSIS; TRANSFER FUNCTIONS; VECTOR QUANTIZATION; WAVELET TRANSFORMS;

DISCRETE TIME VECTOR VALUED SIGNALS; PARAUNITARY VECTOR FILTER BANK THEORY; SCALAR TRANSFORM DOMAIN; UNITARY VECTOR TRANSFORMS; VECTOR VALUED WAVELETS;

DIGITAL FILTERS;

EID: 0030106217     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.489024     Document Type: Article

References (46)

1. X.-G. Xia and B. W. Suter, "Multirate filter banks with block sampling," IEEE Trans. Signal Processing, this issue, pp. 484-496.
2. M. R. K. Khansari and A. Leon-Garcia, "Subband decomposition of signals with generalized sampling," IEEE Trans. Signal Processing, vol. 41, pp. 3365-3376, Dec. 1993.
3. W. Li, "Vector transform and image coding," IEEE Trans. Circuits Syst. Video Technol., vol. 1, pp. 297-307, Dec. 1991.
4. W. Li and Y. Q. Zhang, "A study on the optimal attributes of transform domain vector quantization for image and video compression," ICC, May 1993.
5. W. Li, J. Wus, and Y. Q. Zhang, "New vector subband coding for image and video compression," in Proc. 3rd Symp. Applic. Subbands Wavelets, N. J. Institute of Technology, Newark, NJ, USA, Mar. 1994.
6. W. Li, "On vector transforms," IEEE Trans. Signal Processing, vol. 41, pp. 3114-3126, Nov. 1993.
7. I. Pitas and A. Karasaridis, "Discrete multichannel orthogonal transforms," in IEEE Proc. ICASSP'94, Adelaide, Australia, Apr. 1994, pp. V-325-328.
8. T. N. T. Goodman, S. L. Lee, and W. S. Tang, "Wavelets in wandering subspaces," Trans. Amer. Math. Soc., vol. 338, pp. 639-654, 1993.
9. T. N. T. Goodman and S. L. Lee, "Wavelets of multiplicity r," Trans. Amer. Math. Soc., vol. 342, pp. 307-324, Mar. 1994.
10. J. S. Geronimo, D. P. Hardin, and P. R. Massopust, "Fractal functions and wavelet expansions based on several scaling functions," J. Approx. Theory, 1994.
11. G. Strang and V. Strela, "Short wavelets and matrix dilation equations," IEEE Trans. Signal Processing, vol. 43, pp. 108-115, Jan. 1995.
12. _, "Orthogonal multiwavelets with vanishing moments," in SPIE Proceedings, Orlando, FL, USA, Apr. 1994.
13. M. Vetterli and G. Strang, "Time-varying filter banks and multiwavelets," in Proc. Sixth Digital Signal Processing Workshop, Yosemite, CA, USA, Oct. 1994.
14. C. A. Micchelli and Y. Xu, "Using the matrix refinement equation for the construction of wavelets on invariant sets," to appear in Appl. Comp. Harmonic Anal.
15. _, "Using the matrix refinement equation for the construction of wavelets II: Smooth wavelets on [0], [1]," preprint.
16. Z. Doǧanata, P. P. Vaidyanathan, and T. Q. Nguyen, "General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications," IEEE Trans. Acoust., Speech, Signal Proc., vol. 36, pp. 1561-1574, Oct. 1988.
17. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
18. X.-G. Xia and B. W. Suter, "FIR paraunitary filter banks given several analysis filters: Factorizations and constructions," IEEE Trans. Signal Processing, vol. 44, pp. 720-723, this issue.
19. G.G. Walter, "A sampling theorem for wavelet subspaces," IEEE Trans. Inform. Theory, vol. 38, pp. 881-884, 1992.
20. A. Aldroubi and M. Unser, "Families of wavelet transforms in connection with Shannon's Sampling Theory and the Gabor transform," Wavelets: A Tutorial in Theory and Applications, C.K. Chui, Ed. New York: Academic, 1992, pp. 509-528.
21. A. Aldroubi and M. Unser, "Families of multiresolution and wavelet spaces with optimal properties," Numer. Funct. Anal. Optimiz., vol. 14. pp. 417-446, 1993.
22. X.-G. Xia and Z. Zhang, "On sampling theorem, wavelets and wavelet transforms," IEEE Trans. Signal Processing, vol. 41, pp. 3524-3535, Dec. 1993.
23. O. Rioul and P. Duhamel, "Fast algorithms for discrete and continuous wavelet transform," IEEE Trans. Inform. Theory, vol. 38, pp. 569-586 1992.
24. M. J. Shensa, "The discrete wavelet transform: wedding the Atrous and Mallat algorithm," IEEE Trans. Signal Processing, vol. 40, pp. 2464-2482, Oct. 1992.
25. I. Daubechies, "Orthonormal bases of compactly supported wavelets," Comm. Pure Appl. Math., vol. 41, pp. 909-996, 1988.
26. 2 (R)," Trans. Amer. Math. Soc., vol. 315, pp. 69-87, 1989.
27. S. Mallat, "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Trans. Pattern Anal. and Mach. Intell., vol. 11, pp. 674-693, 1989.
28. G. Strang, "Wavelets and dilation equations: A brief introduction," SIAM Review, vol. 31, pp. 614-627, 1989.
29. C. E. Heil and D. F. Walnut, "Continuous and discrete wavelet transforms," SIAM Rev., vol. 31, pp. 628-666, Dec. 1989.
30. O. Rioul and M. Vetterli, "Wavelets and signal processing," IEEE Signal Proc. Mag., pp. 14-38, Oct. 1991.
31. M. Vetterli and C. Herley, "Wavelets and filter banks: Theory and design," IEEE Trans. Signal Processing, vol. 40, pp. 2207-2232, Sept. 1992.
32. n," IEEE Trans. Inform. Theory, vol. 38, pp. 533-555, Mar. 1992.
33. I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inform. Theory, vol. 36, pp. 961-1005, Sept. 1990.
34. C. K. Chui, An Introduction to Wavelets. Academic: New York, 1992.
35. I. Daubechies, Ten Lectures on Wavelets. SIAM: Philadelphia, 1992.
36. Y. Meyer, Wavelets: Algorithms and Applications. SIAM: Philadelphia, 1993.
37. _, Ondelettes et Opérateurs Paris: Hermann, 1990.
38. Special Issue on Wavelet Transforms and Multiresolution Signal Analysis, IEEE Trans. Inform. Theory, vol. 38, Mar. 1992.
39. Special Issue on Wavelets and Signal Processing, IEEE Trans. Signal Processing, vol. 41, Dec. 1993.
40. M. Vetterli and J. Kovačević, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.
41. L. Hervé, "Multi-resolution analysis of multiplicity d: applications to dyadic interpolation," Appl. Computat. Harmonic Anal., vol. 1, pp. 299-315, 1994.
42. G. Donovan, J. S. Geronimo, D. P. Hardin, and P. R. Massopust, "Construction of orthogonal wavelets using fractal interpolation functions," preprint, 1994.
43. G. Donovan, J. S. Geronimo, and D. P. Hardin, "Intertwining multiresolution analysis and the construction of piecewise polynomial wavelets," preprint, 1994.
44. P. N. Heller, V. Strela, G. Strang, P. Topiwala, C. Heil, and L. S. Hills, "Multiwavelet filter banks for data compression," preprint, 1994.
45. X.-G. Xia, J. S. Geronimo, D. P. Hardin, and B. W. Suter, "Design of prefilters for discrete multiwavelet transforms," IEEE Trans. Signal Processing, vol. 44, pp. 25-35, Jan. 1996.
46. V. M. Gadre and R. K. Patney, "Vector multirate filtering and matrix filter banks," in IEEE Proc. Int. Symp. Circuits Syst., pp. 1360-1363, 1994.