Abstract
This paper discusses the optimal coding of uniformly quantized Laplacian sources. The techniques known for designing optimal codes for sources with infinite alphabets are used for the quantized Laplacian sources which have probability mass functions with two geometrically decaying tails. Due to the simple parametric model of the source distribution the Huffman iterations are possible to be carried on analytically, using the concept of reduced source, and the final codes are obtained as a sequence of very simple arithmetic operations, avoiding the need to store coding tables. Comparing three uniform quantizers, we find one which consistently outperforms the others in the rate-distortion sense. We foresee for the newly introduced codes an important area of applications in low complexity lossy image coding, since similar codes, designed for two-sided geometrical sources, became the basic tools used in JPEG-LS lossless image compression.
Similar content being viewed by others
References
J. Abrahams, “Huffman-type codes for infinite source distributions,” Journal of the Franklin Institute, Elsevier Science, Vol. 331B, No. 3, pp. 265-271, 1994.
J. Abrahams, “Code and parse trees for lossless source encoding,” in: Proc. Compression and Complexity of Sequences, Positano, Salerno, Italy, pp. 145-171, 1997.
T. Berger, “Minimum entropy quantizers and permutation codes,”.IEEE Transactions on Information Theory, Vol. 28, No. 2, pp. 149-157, 1982.
R. Gallager and D. V. Voorhis, “Optimal source codes for geometrically distributed integer alphabets,”.IEEE Transactions on Information Theory Vol. IT-21, pp. 228-230, 1975.
S. Golomb, “Run-length encodings'.IEEE Transactions on Information Theory, Vol. 12, pp. 399-401, 1966.
V. Goyal, “Transform coding with integer-to-integer transforms,”. IEEE Transactions on Information Theory, Vol. 46, No. 2, pp. 465-473, 2000.
P. Humblet, “Optimal source coding for a class of integer alphabets,”.IEEE Transactions on Information Theory, Vol. IT-24, pp. 110-112, 1978.
A. Jain, Fundamentals of digital image processing.Prentice-Hall, Inc., 1989.
N. Jayant, and P. Noll, Digital Coding of Waveforms. Principles and Applications to Speech, Prentice-Hall, Inc., 1984.
N. Merhav, G. Seroussi, and M. Weinberger, “Coding of sources with Two-Sided Geometric distributions with unknown parameters,”.IEEE Transactions on Information Theory, Vol. 46, No. 1, pp. 229-236, 2000a.
N. Merhav, G. Seroussi, and M. Weinberger, “Optimal prefix codes for sources with Two-Sided Geometric Distributions,”. IEEE Transactions on Information Theory, Vol. 46, No. 1, pp. 121-135, 2000b.
R. Rice, “Some practical universal noiseless coding techniques-Parts I-III,” Technical Report JPL-79-22, JPL-83-17 and JPL-91-3, Jet Propulsion Laboratory, Pasadena,California,USA, 1979,1983 and 1991.
G. Sullivan, “Efficient scalar quantization of Exponential and Laplacian random variables,”.IEEE Transactions on Information Theory, Vol. 42, No. 5, pp. 1365-1374, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Doru Giurcăneanu, C., Tăbuş, I. Optimal Coding of Quantized Laplacian Sources for Predictive Image Compression. Journal of Mathematical Imaging and Vision 16, 251–268 (2002). https://doi.org/10.1023/A:1020333827888
Issue Date:
DOI: https://doi.org/10.1023/A:1020333827888