Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-06T10:59:20.493Z Has data issue: false hasContentIssue false

2 - Book overview

Published online by Cambridge University Press:  05 June 2012

William A. Pearlman  and
Amir Said
William A. Pearlman
Affiliation:
Rensselaer Polytechnic Institute, New York
Amir Said
Affiliation:
Hewlett-Packard Laboratories, Palo Alto, California
Get access

Summary

Entropy and lossless coding

Compression of a digital signal source is just its representation with fewer information bits than its original representation. We are excluding from compression cases when the source is trivially over-represented, such as an image with gray levels 0 to 255 written with 16 bits each when 8 bits are sufficient. The mathematical foundation of the discipline of signal compression, or what is more formally called source coding, began with the seminal paper of Claude Shannon [1, 2], entitled “A mathematical theory of communication,” that established what is now called Information Theory. This theory sets the ultimate limits on achievable compression performance. Compression is theoretically and practically realizable even when the reconstruction of the source from the compressed representation is identical to the original. We call this kind of compression lossless coding. When the reconstruction is not identical to the source, we call it lossy coding. Shannon also introduced the discipline of Rate-distortion Theory [1–3], where he derived the fundamental limits in performance of lossy coding and proved that they were achievable. Lossy coding results in loss of information and hence distortion, but this distortion can be made tolerable for the given application and the loss is often necessary and unavoidable in order to satisfy transmission bandwidth and storage constraints. The payoff is that the degree of compression is often far greater than that achievable by lossless coding.

Type
Chapter
Information
Digital Signal Compression
Principles and Practice
 , pp. 10 - 22
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Shannon, C. E., “A mathematical theory of communication,” Bell Syst. Technol. J., vol. 27, pp. 379–423 and 632–656, July and Oct. 1948.CrossRefGoogle Scholar
2. Shannon, C. E. and Weaver, W., The Mathematical Theory of Communication. Urbana, IL: University of Illinois Press. 1949.Google Scholar
3. Shannon, C. E., “Coding theorems of a discrete source with a fidelity criterion,” in Information and Decision Processes, ed. Machol, R. E.New York, NY: McGraw-Hill Publishing Co., 1960, pp. 93–126.Google Scholar
4. Rao, R. P. and Pearlman, W. A., “On entropy of pyramid structures,” IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 407–413, Mar. 1991.CrossRefGoogle Scholar
5. Woods, J. W. and O'Neil, S. D., “Subband coding of images,” IEEE Trans. Acoust. Speech Signal Process., vol. 34, no. 5, pp. 1278–1288, Oct. 1986.CrossRefGoogle Scholar
6. Crochiere, R. E., Webber, S. A., and Flanagan, J. L., “Digital coding of speech in sub-bands,” in Proceedings of the IEEE International Conference on Acoustics Speech Signal Processing, Philadelphia, PA, Apr. 1976, pp. 233–236.Google Scholar
7. Pearlman, W. A., “Performance bounds for subband coding,” in Subband Image Coding, ed. Woods, J. W.Norwell, MA: Kluwer Academic Publishers. 1991, ch. 1.Google Scholar
8. Rao, S. and Pearlman, W. A., “Analysis of linear prediction, coding, and spectral estimation from subbands,” IEEE Trans. Inf. Theory, vol. 42, no. 4, pp. 1160–1178, July 1996.CrossRefGoogle Scholar
9. Chai, B.-B., Vass, J., and Zhuang, X., “Significance-linked connected component analysis for wavelet image coding,” IEEE Trans. Image Process., vol. 8, no. 6, pp. 774–784, June 1999.CrossRefGoogle ScholarPubMed
Girod, B., Aaron, A. M., Rane, S., and Rebollo-Monedero, D., “Distributed video coding,” Proc. IEEE, vol. 91, no. 1, pp. 71–83, Jan. 2005.CrossRefGoogle Scholar
Hong, E. S. and Ladner, R. E., “Group testing for image compression,” IEEE Trans. Image Process., vol. 11, no. 8, pp. 901–911, Aug. 2002.CrossRefGoogle ScholarPubMed
Pearlman, W. A., Islam, A., Nagaraj, N., and Said, A., “Efficient, low-complexity image coding with a set-partitioning embedded block coder,” IEEE Trans. Circuits Syst. Video Technol., vol. 14, no. 11, pp. 1219–1235, Nov. 2004.CrossRefGoogle Scholar
Pradhan, S. S., Kusuma, J., and Ramchandran, K., “Distributed compression in a dense microsensor network,” IEEE Signal Process. Mag., pp. 51–60, Mar. 2002.CrossRefGoogle Scholar
Said, A. and Pearlman, W. A., “A new, fast, and efficient image codec based on set partitioning in hierarchical trees,” IEEE Trans. Circuits Syst. Video Technol., vol. 6, no. 3, pp. 243–250, June 1996.CrossRefGoogle Scholar
Shapiro, J. M., “Embedded image coding using zerotrees of wavelet coefficients,” IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3445–3462, Dec. 1993.CrossRefGoogle Scholar
Taubman, D. S., “High performance scalable image compression with EBCOT,” IEEE Trans. Image Process., vol. 9, no. 7, pp. 1158–1170, July 2000.CrossRefGoogle ScholarPubMed

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Book overview
  • William A. Pearlman, Rensselaer Polytechnic Institute, New York, Amir Said, Hewlett-Packard Laboratories, Palo Alto, California
  • Book: Digital Signal Compression
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511984655.003
Available formats
×