Abstract
The purpose of this chapter is to present some tutorial material in information theory which is pertinent to the subject of subband coding and to develop this material further in order to gain insight into the superior performance realized in subband coding systems. Except for the well-known result that PCM coding of subbands outperforms direct PCM coding of the full-band original (see [7]), which is known to be generally inefficient, there have been hardly any theoretical analyses which have shown a mean-squared error improvement for subband coding. The superior results of subband coding systems are largely empirical in nature and they have indeed been impressive in coding of images. In this chapter these superior results are quantified in formulas, which have not yet appeared in print elsewhere.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
D.A. Huffman, “A method for construction of minimum redundancy codes”, Proc. IRE, vol. 40, pp. 1098–1101, Sept. 1952.
R.E. Blahut, “Computation of channel capacity and rate-distortion function”, IEEE Trans. Inform. Theory, vol. IT-18, pp. 460–473, July 1972.
R.G. Gallager, Information Theory and Reliable Communication, New York: J. Wiley and Sons, Inc., 1968.
W.A. Pearlman and P. Jakatdar, “A transform tree code for stationary Gaussian sources”, IEEE Trans. Inform. Theory, vol. IT-31, pp. 761–768.
B. Mazor and W.A. Pearlman, “A trellis code construction and coding theorem for stationary Gaussian sources”, IEEE Trans. Inform. Theory, vol. IT-29, pp. 924–930, Nov. 1983.
B. Mazor and W.A. Pearlman, “A tree coding theorem for stationary Gaussian sources and the squared-error distortion measure”, IEEE Trans. Inform. Theory, vol. IT-32, pp. 156–165, March 1986.
N.S. Jayant and P. Noll, Digital Coding of Waveforms, Englewood Cliffs, NJ: Prentice Hall, 1984.
R. Bellman, Introduction to Matrix Analysis, 2nd Ed., New York: McGraw-Hill, 1970.
S. Nanda, A Tree Coding Theorem and Tree Coding of Subbands with Application to Images, Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, NY, October 1988.
P.H. Westerink, “An optimal bit allocation for subband coding”, Proc. 1988 IEEE Int. Conf. Acoust., Speech, Signal Process., New York, April 1988, pp. 757–760.
J.W. Woods and S.D. O’Neil, “Subband coding of images”, IEEE Trans. Acoustics, Speech, and Signal Processing, vol. ASSP-34, pp. 1278–1286, October 1986.
A.D. Wyner and J. Ziv, “Bounds on the rate-distortion function for stationary sources with memory”, IEEE Trans. Inform. Theory, vol. IT- 17, pp. 508–513, September 1971.
R.P. Rao and W.A. Pearlman, “On entropy rate for source encoding on a pyramid structure”, Abstracts of 1990 IEEE International Symposium on Information Theory, January 1990, San Diego, CA, pp. 57–58; also R.P. Rao and W.A. Pearlman, “On entropy rate of pyramid structures”, submitted to IEEE Trans. Inform. Theory.
P. Chou, T. Lookabaugh, and R.M. Gray, “Optimal pruning with applications to treestructured source coding and modeling”, IEEE Trans. Inform. Theory, vol. IT-35, pp. 299–315, March 1989.
L. Breiman, J.H. Friedman, R.A. Olshen, and C.J. Stone, Classification and Regression Trees, Monterey, CA: Wadsworth, 1984.
B. Mahesh and W.A. Pearlman, “Multiple rate code book design for vector quantization of image pyramids”, Applications of Digital Image Processing XIII, A. Tescher, Ed., Proc. SPIE 1349, July 1990.
J.W. Modestino, V. Bhaskaran, and J.B. Anderson, “Tree encoding of images in the presence of channel errors”, IEEE Trans. Inform. Theory, vol. IT-27, pp. 677–697, Nov. 1981.
J.B. Anderson and J.B. Brodie, “Tree encoding of speech”, IEEE Trans. Inform. Theory, vol. IT-21, pp. 379–387, July 1975.
H.G. Fehn and P. Noll, “Multipath search coding of stationary signals with applications to speech”, IEEE Trans. Commun., vol. COM-30, pp. 687–701, April 1982.
P. Kroon and E.F. Deprettere, “A class of analysis-by-synthesis predictive coders for high quality speech coding at rates between 4.8 and 16 kbits/s”, IEEE J. Select. Area Commun., vol. 6, pp. 353–363, Feb. 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Pearlman, W.A. (1991). Performance Bounds for Subband Coding. In: Woods, J.W. (eds) Subband Image Coding. The Springer International Series in Engineering and Computer Science, vol 115. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2119-5_1
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2119-5_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5123-6
Online ISBN: 978-1-4757-2119-5
eBook Packages: Springer Book Archive