On the Optimality of Ideal Filters for Pyramid and Wavelet Signal Approximation

IEEE Transactions on Signal Processing

Volumn 41, Issue 12, 1993, Pages 3591-3596

  Unser, Michael ^a  

^a NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; LEAST SQUARES APPROXIMATIONS; LOW PASS FILTERS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; SIGNAL THEORY; SPECTRUM ANALYSIS;

IDEAL FILTERS; MULTIRESOLUTION TECHNIQUES; PYRAMID DECOMPOSITION;

SIGNAL FILTERING AND PREDICTION;

EID: 0027814843     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.258103     Document Type: Article

References (22)

1. S. G. Mallat, “A theory of multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Patt. Anal. Mach. Intel!., vol. 11, pp. 674–693, 1989.
2. O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Mag., vol. 8, pp. 11–38, Oct. 1991.
3. O. Rioul, “A discrete-time multiresolution theory,” IEEE Trans. Signal Processing, vol. 41, pp. 2591–2606, Aug. 1993.
4. M. Vetterli, “Multidimensional subband coding: Some theory and algorithms,” Signal Processing, vol. 6, pp. 97–112, Apr. 1984.
5. V. K. Jain and R. E. Crochiere, “Quadrature mirror filter design in the same domain,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-32, pp. 353–361, Apr. 1984.
6. P. P. Vaidyanathan and P.-Q. Hoang, “Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-36, pp. 81–94, 1988.
7. P. Desarte, B. Macq, and D. T. M. Slock, “Signal-adapted multiresolution transform for image coding,” IEEE Trans. Informat. Theory, vol. 38, pp. 897–904, Mar. 1992.
8. A. H. Tewfik, D. Sinha, and P. Jorgensen, “On the optimal choice of a wavelet for signal representation,” IEEE Trans. Informat. Theory, vol. 38, pp. 747–765, 1992.
9. P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact code,” IEEE Trans. Commun., vol. COM-31, pp. 337–345, Apr. 1983.
10. M. Unser, “An improved least squares Laplacian pyramid for image compression,” Signal Processing, vol. 27, pp. 187–203, May 1992.
11. G. C. Gurski, M. T. Orchard, and A. W. Hull, “Optimal linear filters for pyramidal decomposition,” in Proc. Int. Conf. Acoust., Speech, and Signal Processing, San Francisco, CA, March 23–26, 1992, pp. 633–636.
12. M. J. T. Smith and T. P. Barnwell, “Exact reconstruction for tree-structured subband coders,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. ASSP-34, pp. 423–441, June 1986.
13. I. Daubechies, “Orthogonal bases of compactly supported wavelets,” Commun. Pure Appl. Math., vol. 41, pp. 909–996, 1988.
14. K. M. Uz, M. Vetterli, and D. J. LeGall, “Interpolative multiresolution coding of advanced television with compatible subchannel,” IEEE Trans. Circuits Syst. Video Tech., vol. 1, pp. 86–99, Mar. 1991.
15. M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing. Part II: Efficient design and applications,” IEEE Trans. Signal Processing, vol. 41, pp. 834–848, Feb. 1993.
16. M. Unser, A. Aldroubi, and M. Eden, “Discrete spline filters for multiresolutions and wavelets of l 2,” SIAM J. Math. Anal., to appear.
17. M. Antonini, M. Barlaud, P. Mathieu and I. Daubechies, “Image coding using wavelet transform,” IEEE Trans. Image Processing, vol. 1, pp. 205–220, Apr. 1992.
18. A. Aldroubi and M. Unser, “Sampling procedures in function spaces and asymptotic equivalence with Shannon's sampling theory,” Numer. Functional Anal, and Optimization, to appear.
19. A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 1991.
20. P.-G. Lemarié, “Ondelettes a localisation exponentielles,” J. Math, pures et appl., vol. 67, pp. 227–236, 1988.
21. A. Aldroubi and M. Unser, “Families of multiresolution and wavelet spaces with optimal properties,” Numer. Functional Anal, and Optimization, vol. 14, pp. 417–446, 1993.
22. M. K. Tsatsanis and G. B. Giannakis, “Principal component filter banks for optimal wavelet analysis,” submitted to IEEE Trans. Signal Processing. Also, Proc. 6th Signal Processing Workshop on Statistical Signal and Array Processing, Victoria, B.C., Canada, Oct. 7–9, 1992, pp. 193–196.