Signal processing using cellular neural networks

  • L. O. Chua
  • L. Yang
  • K. R. Krieg


The cellular neural network (CNN) architecture combines the best features from traditional fully-connected analog neural networks and digital cellular automata. The network can rapidly process continuous-valued (gray-scale) input signals (such as images) and perform many computation functions which traditionally were implemented in digital form. Here, we briefly introduce the the theory of CNN circuits, provide some examples of CNN applications to image processing, and discuss work toward a CNN implementation in custom CMOS VLSI. The role of analog computer-aided design (CAD) will be briefly presented as it relates to analog neural network implementation.


Radon Input Image Cellular Automaton Noise Removal Feedback Operator 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.J. Hopfield, “Neural networks and physical systems with emergent computational abilities”,Proc. Natl. Acad. Sci. USA, vol. 79, 1982, pp. 2554–2558.MathSciNetCrossRefGoogle Scholar
  2. 2.
    J.J. Hopfield and D. W. Tank, “Computing with neural circuits: a model,”Science (USA), vol. 233, no. 4764, 1986, pp. 625–633.Google Scholar
  3. 3.
    D.E. Rumelhart and J.L. McClelland,Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1: Foundations, Cambridge, MA: M.I.T. Press, 1986.Google Scholar
  4. 4.
    K. Preston, Jr., and M. J. B. Duff,Modern Cellular Automata: Theory and Applications, New York: Plenum Press, 1984.CrossRefMATHGoogle Scholar
  5. 5.
    T. Toffoli and N. Margolus,Cellular Automata Machines—a new environment for modeling, Cambridge, MA: M.I.T. Press, 1986.Google Scholar
  6. 6.
    J. von Neumann,The Computer and the Brain, New Haven: Yale University Press, 1958.MATHGoogle Scholar
  7. 7.
    J. von Neumann, “The general logical theory of automata,”Cerebral Mechanisms in Behavior—The Hixon Symposium, New York: Wiley, 1951.Google Scholar
  8. 8.
    S. Wolfram,Theory and applications of cellular automata, World Scientific Publishing Co., 1986.Google Scholar
  9. 9.
    L.O. Chua and L. Yang, “Cellular Neural Networks: Theory,”IEEE Trans. Circuits and Systems, vol. 35, no. 10, 1988, pp. 1257–1272.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    L.O. Chua and L. Yang, “Cellular Neural Networks: Applications,”IEEE Trans. Circuits and Systems, vol. 35, no. 10, 1988, pp. 1273–1290.MathSciNetCrossRefGoogle Scholar
  11. 11.
    L.O. Chua, C.A. Desoer, and E.S. Kuh,Linear and Nonlinear Circuits, New York: McGraw-Hill, 1987.MATHGoogle Scholar
  12. 12.
    L.O. Chua,Introduction to Nonlinear Network Theory, New York: McGraw-Hill, 1970, (987 pages)Google Scholar
  13. 13.
    L.O. Chua and P.M. Lin,Computer-aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Englewood Cliffs, NJ: Prentice Hall 1975, p. 72.MATHGoogle Scholar
  14. 14.
    L.O. Chua and R. Ying, “Finding All Solutions of Piecewise-Linear Circuits,”International Journal of Circuit Theory and Applications, vol. 10, 1982, pp. 201–229.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    J. Hopfield and D. Tank, “Neural' Computation of Decisions in Optimization Networks,”Biological Cybernetics, vol. 52, 1985, pp. 141–152.MathSciNetMATHGoogle Scholar
  16. 16.
    J. Hopfield and D. Tank, “Collective Computation with Continous Variables,” inDisordered Systems and Biological Organization, (ed. E. Bienenstock, F. Fogelman & G. Weisbuch), Berlin: Springer-Verlag, 1985.Google Scholar
  17. 17.
    R.L. McEleice, E.C. Posner, E.R. Rodemich, and S.S. Venkatesh, “The Capacity of the Hopfield Associative Memory,”IEEE Trans. on Information Theory vol. IT-33, no. 4, 1987, pp. 461–482.CrossRefGoogle Scholar
  18. 18.
    L.O. Chua and T. Roska, “Stability of a Class of Nonreciprocal Cellular Neural Networks,”IEEE Trans. on Circuits and Systems, vol. 37, 1990, pp. 1520–1527.CrossRefGoogle Scholar
  19. 19.
    W.S. McCulloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,”Bulletin of Mathematical Bioophysics, vol. 5, 1943, pp. 115–133.MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    W. Pitts and W. McCulloch, “How we know universals: the perception of auditory and visual forms,”Bulletin of Mathematical Biophysics, vol. 9, 1947, pp. 127–147.CrossRefGoogle Scholar
  21. 21.
    H.D. Block, “The Perceptron: a model for brain functioning. I,”Reviews of Modern Physics, vol. 34, 1962, pp. 123–135.MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    M. Minsky and S. Papert,Perceptrons: An Introduction of Computational Geometry, Cambridge, MA: M.I.T. Press, 1969.MATHGoogle Scholar
  23. 23.
    T. Matsumoto, L.O. Chua, and H. Suzuki, “CNN Cloning Template: Connected Component Detector,IEEE Trans. on Circuit and Systems, vol. 37, 1990, pp. 633–635.MathSciNetCrossRefGoogle Scholar
  24. 24.
    M.P. Kennedy and L.O. Chua, “Circuit Theoretic Solutions for Neural Networks—an old approach to a new problem,”Proc. First ICNN, vol. 2, San Diego, CA: IEEE, 1987, pp. 169–176.Google Scholar
  25. 25.
    M.J.B. Duff and T.J. Fountain,Cellular Logic Image Processing, London: Academic Press, 1986.Google Scholar
  26. 26.
    Anil K. Jain,Fundamentals of Digital Image Processing, Englewood Cliffs, NJ: Prentice-Hall, 1989.MATHGoogle Scholar
  27. 27.
    L.O. Chua and B. Shi,Exploiting Cellular Automata in the Design of Cellular Neural Networks for Binary Image Processing, UCB/ERB M89/130, November 15, 1989.Google Scholar
  28. 28.
    T. Kohonen,Self-Organization and Associative Memory New York: Springer-Verlga, 1984.MATHGoogle Scholar
  29. 29.
    T. Matsumoto, L.O. Chua and T. Yokohama, “Image Thinning With A cellular Neural Network,”IEEE Trans. on Circuits and Systems, vol. 37, 1990, pp. 638–640.CrossRefGoogle Scholar
  30. 30.
    P.M. Morse and H. Feshback,Methods of Theoretical Physics, Part I, New York: McGraw-Hill, 1953.Google Scholar
  31. 31.
    M.A. Sivilotti, M.A. Mahowald, and C.A. Mead, “Real-time visual computations using analog CMOS processing arrays,”Advanced Research in VLSI: Proceedings of the 1987 Stanford Conference. Cambridge, MA: M.I.T. Press, 1987, p. 295.Google Scholar
  32. 32.
    T. Matsumoto, L.O. Chua, and Furukawa, “CNN Cloning Template: Hole Filler,”IEEE Trans. on Circuits and Systems, vol. 37, pp. 635–638.Google Scholar
  33. 33.
    Proceedings of the 1990 IEEE International Workshop on Cellular Neural Networks and Their Applications, December 16–19, 1990, Budapest, Hungary.Google Scholar
  34. 34.
    J.M. Cruz and L.O. Chua, “A CNN chip for connected component detection,”IEEE Trans. on Circuits and Systems, vol. 38, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • L. O. Chua
    • 1
  • L. Yang
    • 1
  • K. R. Krieg
    • 1
  1. 1.Dept. of EECSUniversity of CaliforniaBerkeley

Personalised recommendations