Advertisement

Dimensionality Reduction and Quantization

Abstract

The dilemma of information processing is that the states of the environment, and consequently the primary information are continuous but that digital information processing is efficient and cheap. Section 1.5.4 described the basic transformations of the primary continuous information into discrete information. Such a transformation is called discretization; discretization of scalar or vector information is called1 quantization. The important types of discretization are listed in Figure 1.22.

Keywords

Dimensionality Reduction Spectral Representation Spectral Component Primary Information Harmonic Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [7.1]
    Thompson, E.E., An Introduction to Algebra of Matrices with some Applications, Adam Hilger, London, 1969.MATHGoogle Scholar
  2. [7.2]
    Horn, R.A., Johnson C.,R., Matrix Analysis, Cambridge University Press, Cambridge 1988.Google Scholar
  3. [7.3]
    Usmani, R.A., Applied Linear Algebra, Marcel Decker, N.Y, 1987.MATHGoogle Scholar
  4. [7.4]
    Poularikas, A.D., The Transforms and Applications Handbook, IEEE Press, N.Y., 1995.Google Scholar
  5. [7.5]
    Smith, W.W., Smith, J.M., The Handbook of Real-Time Fast Fourier Transforms, IEEE Press, N.Y., 1995.Google Scholar
  6. [7.6]
    Press, W.H., Flannery, B.P., Teukolsy, S.A., Vetterling, W.T., Numerical Recipes, Cambridge University Press, Cambridge, 1992.Google Scholar
  7. [7.7]
    Curtain, R., Pritchard, A.J., Functional Analysis in Modern Applied Mathematics, Academic Press, N.Y, 1977.MATHGoogle Scholar
  8. [7.8]
    Mallat, S.G., “A Theory of Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE Trans. on Pattern Analysis And Machine Intelligence, vol 11 (1989) pp. 674–693.MATHCrossRefGoogle Scholar
  9. [7.9]
    Oppenheim, A.V., Wilsky A., S., Signals and Systems, Prentice Hall, Englewood Cliffs, NJ 1989.Google Scholar
  10. [7.10]
    Lim, J.S., Two-Dimensional Signal and Image Processing, Prentice Hall, Englewood Cliffs, NJ, 1990.Google Scholar
  11. [7.11]
    Schalkoff, R.J., Digital Image Processing And Computer Vision, J. Viley, NY, 1989.Google Scholar
  12. [7.12]
    Russ, J.C., ed., The Image Processing Handbook, (2-nd ed.), IEEE Press, NY, 1994.Google Scholar
  13. [7.13]
    Rioul, O., Vetterli, M., “Wavelets And Signal Processing”, IEEE SP Magazine, October 1991, pp. 14–38.Google Scholar
  14. [7.14]
    Young, R.,K., Wavelet Theory and Applications, SIAM Press, Philadelphia, 1993.Google Scholar
  15. [7.15]
    Wickerhauser, M.V., Adapted Wavelet Analysis From Theory To Practice, IEEE Press, NY, 1996Google Scholar
  16. [7.16]
    Vetterli, M., Kovacevic, J., Wavelts And Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.Google Scholar
  17. [7.17]
    Chui, K.C., ed., Wavelets: A tutorial In Theory And Applications, Academic Press, NY, 1991.Google Scholar
  18. [7.18]
    Papoulis, R., Probability, Random Variables, and Stochastic Processes, McGraw-Hill, N.Y., 1991.Google Scholar
  19. [7.19]
    Blanc-Lapierre, B., Fortet R., Theory of Random Functions, vol 1,2 Gordon and Breach, N.Y., 1967.MATHGoogle Scholar
  20. [7.20]
    Gersho, A., Gray, B., and Gray, R.M., Vector Quantization And Signal Comression, Kluwer, Boston, 1992.Google Scholar
  21. [7.21]
    Abut H., ed. Vector Quantization, IEEE Press, NY, 1996.Google Scholar
  22. [7.22]
    Nelson, M., The Data Compression Book, M&T Books, Redwood City, CA, 1991.MATHGoogle Scholar
  23. [7.23]
    Storer, J.A., Reif, J.H., DCC’91 Data Compression Conference, IEEE Computer Society Press, Los Alamitos, CA, 1991.Google Scholar
  24. [7.24]
    Storer, J.A., Cohn, M., DCC’92 Data Compression Conference, IEEE Computer Society Press, Los Alamitos, CA, 1992.Google Scholar
  25. [7.25]
    Storer, J.A., Cohn, M., DCC’93 Data Compression Conference, IEEE Computer Society Press, Los Alamitos, CA, 1993.Google Scholar
  26. [7.26]
    Storer, J.A., Cohn, M., DCC’94 Data Compression Conference, IEEE Computer Society Press, Los Alamitos, CA, 1994.Google Scholar
  27. [7.26]
    ICIP-94 Proceedings, IEEE Computer Society Press, Los Alamitos, CA, 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Personalised recommendations