Optimal Wavelet Representation of Signals and the Wavelet Sampling Theorem

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing

Volumn 41, Issue 4, 1994, Pages 262-277

  Gopinath, R A ^a   Odegard, J E ^a   Burrus, C S ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

optimal multiresolution; optimal wavelet design; wavelet sampling theorem; wavelets

Indexed keywords

EID: 84944020690     PISSN: 10577130     EISSN: None     Source Type: Journal    
DOI: 10.1109/82.285705     Document Type: Article

References (32)

1. M. Antonini et al. “Image coding using the wavelet transform,” IEEE Trans. on Image Proc., vol. 2, no. 2, April 1992.
2. A. Barbé, “A level-crossing based scaling-dimensionality transform applied to stationary gaussian processes” IEEE Trans. Inform. Theory, vol. 38, no. 2, p. 814–823, Mar. 1992.
3. M. Basseville et al. “Modeling and estimation of multiresolution stochastic process,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 766–784, Mar. 1992.
4. A. Cohen et al., “Biorthogonal bases of compactly supported wavelets,” Comm. Pure Applied Math., 1992.
5. R. R. Coifman and M. V. Wickerhauser, “Entropy-based algorithms for best basis selection,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 1713–1716, 1992.
6. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. Pure Applied Math., vol. 41, pp. 909–996, Nov. 1988.
7. I. Daubechies, “Ten Lectures on Wavelets,” SIAM, Philadelphia, PA, 1992. Notes from the 1990 CBMS-NSF Conf. on Wavelets and Applications at Lowell, MA.
8. J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1st ed., 1983.
9. R. A. DeVore et al. “Image compression through wavelet transform coding” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 719-746 Mar. 1992.
10. T. Eirola, “Sobolev characterization of solutions of dilation equations,” SIAM J. MATH, vol. 23, no. 4, pp. 1015–1030, July 1992.
11. R. A. Gopinath. Wavelet and Filter Banks - New Results and Applications. Ph.D. thesis, Rice University, Houston, TX, 1992.
12. R. A. Gopinath and C. S. Burrus, “State-space approach to multiplicity M orthonormal wavelet bases,” Technical Report CML TR91-22, Computational Mathematics Laboratory, Rice University, 1991.
13. R. A. Gopinath and C. S. Burrus, “On the moments of the scaling function Ψ0, In Proc. of the IEEE ISCAS, vol. 2, San Diego, CA, May 1992, pp. 963–966. Also Tech. Report CML-TR91-05.
14. R. A. Gopinath and C. S. Burrus, “Wavelet-based lowpass/bandpass interpolation. In Proc. Int. Conf. Acoust., Speech, Sig. Proc., vol. 4, pp. IV385-IV388, San Francisco, CA, Mar. 1992. IEEE. Also Tech. Report CML-TR91-06.
15. R. A. Gopinath and C. S. Burrus, “Wavelets and filter banks,” In Wavelets: A Tutorial in Theory and Applic. Charles K. Chui, Ed., San Diego, CA: Academic Press, 1992, pp. 603–654. Also Tech. Report CML-TR91-20, Sept. 1991.
16. P. Heller, “Regular M-band wavelets,” Tech. Rep. AD920608, Cambridge, MA: Aware Inc., 1992.
17. P. Heller et al. “Wavelet matrices and representation of discrete functions,” In Wavelets: A Tutorial in Theory and Applications, C. K. Chui, Ed., Academic Press, 1992, pp. 15–51.
18. P. Heller and R. O. Wells, Jr., “Spectral theory of multiresolution operators and applications,” In Proc. Int. Conf. on Wavelets, Taormina, Italy, 1993. Also Rice University Tech. Report CML TR93-09.
19. F. Jones “Lebesgue Integration on Euclidean Space,” Boston, MA: Jones and Bartlett, 1993.
20. W. M. Lawton, “Necessary and sufficient conditions for constructing orthonormal wavelet bases,” J. Math. Physics, vol. 32, no. 1, pp. 57–61, Jan. 1991. Also Aware, Inc. Tech. Report AD900402, Apr. 1990.
21. W. R. Madych, “Some elementary properties of multiresolution analyses of ℓ2(Rn),”In Wavelets: A Tutorial in Theory and Applications, C. K. Chui, Ed., Academic Press, 1992, pp. 259-294.
22. P. Moulin et al. “A method of sieves for multiresolution spectrum estimation and radar imaging,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 801–813, Mar. 1992.
23. J. E. Odegard et al., “Optimal wavelets for signal decomposition and the existence of scale limited signals,” In IEEE Proc. Int. Conf. Acoust., Speech, Sig. Proc., vol. 4, pp. 597–600, San Francisco, CA, Mar. 1992.
24. L. Rabiner and B-H. Juang, “Fundamentals of Speech Recognition,” Prentice-Hall, 1993.
25. W. Rudin, “Real and Complex Analysis,” McGraw-Hill., third ed., 1987.
26. P. Steffen, “Closed-form derivation of orthogonal wavelet bases for arbitrary integer scales,” Tech. rep., University of Erlangen-Nümberg, Germany, 1992.
27. P. Steffen et al., “Theory of regular M-band wavelet bases,” IEEE Trans. SP, vol. 41, no. 12, Dec. 1993. Special Transactions on wavelets; Rice contribution also in Tech. Rep. no. CML TR-91-22, Nov. 1991.
28. E. M. Stein and G. Weiss, “Introduction to Fourier Analysis on Euclidean Spaces,” Princeton, NJ: Princeton University Press, 1975.
29. A. H. Tewfik et al., “On the optimal choice of a wavelet for signal representation,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 747–765, Mar. 1992.
30. M. Vetterli, “A theory of multirate filter banks,” IEEE Trans. ASSP, vol. 35, no. 3, pp. 356–372, Mar. 1987.
31. G. W. Womell and A. V. Oppenheim, “Wavelet-based representations for a class of selfsimitar signals with application to fractal modulation,” IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 785–800, Mar. 1992.
32. H. Zou and A. H. Tewfik, “Discrete orthogonal M-band wavelet decompositions,” In IEEE Proc. Int. Conf. Acoust., Speech, Sig. Proc., vol. 4, San Francisco, CA, pp. 605–608, 1992.