Lagrangian vector quantization with combined entropy and codebook size constraints

IEEE Transactions on Information Theory

Volumn 54, Issue 5, 2008, Pages 2220-2242

  Gray, Robert M ^a   Linder, Tamás ^b   Gill, John T ^a  

^a Stanford University   (United States)

^b QUEEN S UNIVERSITY   (Canada)

Author keywords

Asymptotic; Entropy constrained; High rate; Lagrangian; Quantization

Indexed keywords

APPROXIMATION THEORY; CODES (SYMBOLS); LAGRANGE MULTIPLIERS; OPTIMIZATION;

CODEBOOK; LLOYD QUANTIZER DESIGN;

VECTOR QUANTIZATION;

EID: 43749084398     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.920205     Document Type: Article

References (25)

1. A. Aiyer, K.-S. Pyun, Y.-Z. Huang, D. B. O'Brien, and R. M. Cray, "Lloyd clustering of Gauss mixture models for image compression and classifiontion," Signal Process.: Image Commun., vol. 20, pp. 459-485, Jun. 2005.
2. R. B. Ash, Real Analysis and Probability. New York: Academic, 1972.
3. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
4. J. A. Bucklew and G. L. Wise, "Multidimensional asymptotic quantization theory with τth power distortion measures," IEEE Trans. Inf. Theory vol. IT-28, no. 2, pp. 239-247, Mar. 1982.
5. J. A. Bucklew, "Two results on the asymptotic performance of quantizers," IEEE Trans. Inf. Theory, vol. IT-30, no. 2, pp. 341-348, Mar. 1984.
6. W.-Y. Chan and A. Gersho, "Constrained-storage vector quantization in high fidelity audio transform coding," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., Toronto, ON, Canada, May 1991, p. 3597-3600.
7. W.-Y. Chan and A. Gersho, "Enhanced multistage vector quantization by joint codebook design," IEEE Trans. Commun., vol. 40, no. 11, pp. 1693-1697, Nov. 1992.
8. P. A. Chou T. Lookabaugh, and R. M. Gray, "Entropy-constrained vector quantization," IEEE Trans. Acoust. Speech Signal Process., vol. 37, no. 1, pp. 31-42, Jan. 1989.
9. I. Csiszár, "Generalized entropy and quantization problems," in Proc. 6th Prague Conf. Inf. Theory, Statist. Decision Functions, Random Processes, 1973, pp. 159-174.
10. A. Gersho, "Asymptotically optimal block quantization," IEEE Trans. Inf. Theory, vol. IT-25, no. 4, pp. 373-380, Jul. 1979.
11. S. Graf and H. Luschgy, "Foundations of quantization for probability distribution," in Lecture Notes in Mathematics. Berlin, Germany: Springer-Verlag, 2000, vol. 1730.
12. R. M. Gray, T. Linder, and J. Li, "A Lagrangian formulation of Zador's entropy-constrained quantization theorem," IEEE Trans. Inf. Theory vol. 48, no. 3, pp. 695-707, Mar. 2002.
13. R. M. Gray and T. Linder, "Mismatch in high rate entropy constrained vector quantization," IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1204-1217, May 2003.
14. R. M. Gray and T. Linder, "Results and conjectures on high rate quantization," in Proc. Data Compress. Conf., Snowbird, UT, 2004, pp. 3-12.
15. R. M. Gray and J. T. Gill, III, "A Lagrangian formulation of fixed rate and entropy/memory constrained quantization," in Proc. IEEE Data Compress. Conf., Mar. 23-31, 2005, pp. 223-235 [Online]. Available: http://ee.stanford.edu/~gray/dcc05.pdf
16. R. M. Gray and D. L. Neuhoff, "Quantization," IEEE Trans. Inf. Theory, vol. 44, no. 10, pp. 2325-2384, Oct. 1998.
17. A. György, T. Linder, P. A. Chou, and B. J. Betts, "Do optimal entropy-constrained quantizers have a finite or infinite number of code-words?," IEEE Trans. Inf. Theory, vol. 49, no. 11, pp. 3031-3037, Nov. 2003.
18. T. Linder and K. Zeger, "Asymptotic entropy constrained performance of tessellating and universal randomized lattice quantization," IEEE Trans. Inf. Theory, vol. 40, no. 2, pp. 575-579, Mar. 1994.
19. S. P. Lloyd, "Last squares quantization in PCM," IEEE Trans. Inf. Theory, vol. IT-28, no. 2, pp. 129-137, Mar. 1982.
20. S. Na and D. L. Neuhoff, "Bennett's integral for vector quantizers," IEEE Trans. Inf. Theory, vol. 41, no. 4, pp. 886-900, Jul. 1995.
21. R. P. Rao and W. A. Pearlman, "Alphabet-constrained vector quantization," IEEE Trans. Inf. Theory, vol. 39, no. 4, pp. 1167-1179, Jul. 1993.
22. R. L. Wheeden and A. Z. Zygmund, Measure and Integral. New York: Marcel Dekker, 1977.
23. S. Yoon and R. M. Gray, "Clustering and finding the number of clusters by unsupervised learning of mixture models using vector quantization," in Proc. Int. Conf. Acoust. Speech Signal Process., Honolulu, HI, Apr. 2007, vol. 3, pp. 1081-1084.
24. P. L. Zador, "Topics in the asymptotic quantization of continuous random variables," Bell Labs. Tech. Memorandum, 1966.
25. P. L. Zador, "Asymptotic quantization error of continous signals and the quantization dimension," IEEE Trans. Inf. Iheory, vol. IT-28, no. 2, pp. 139-148, Mar. 1982.