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Applied Optics

Applied Optics


  • Vol. 29, Iss. 32 — Nov. 10, 1990
  • pp: 4798–4805

Feedback network with space invariant coupling

Gerd Häusler and Eberhard Lange  »View Author Affiliations

Applied Optics, Vol. 29, Issue 32, pp. 4798-4805 (1990)

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Processing images by a neural network means performing a repeated sequence of operations on the images. The sequence consists of a general linear transformation and a nonlinear mapping of pixel intensities. The general (shift variant) linear transformation is time consuming for large images if done with a serial computer. A shift invariant linear transformation can be implemented much easier by fast Fourier transform or optically, but the shift invariant transform has fewer degrees of freedom because the coupling matrix is Toeplitz. We present a neural convolution network with shift invariant coupling that nevertheless exhibits autoassociative restoration of distorted images. Besides the simple implementation, the network has one more advantage: associative recall does not depend on object position.

© 1990 Optical Society of America

Original Manuscript: August 29, 1989
Published: November 10, 1990

Gerd Häusler and Eberhard Lange, "Feedback network with space invariant coupling," Appl. Opt. 29, 4798-4805 (1990)

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  1. G. Häusler, G. Seckmeyer, T. Weiss, “Chaos and Cooperation in Nonlinear Pictorial Feedback Systems. 1: Experiments,” Appl. Opt. 25, 4656–4663 (1986). [CrossRef] [PubMed]
  2. R. P. Lippmann, “An Introduction to Computing with Neural Nets,” IEEE ASSP Magezin 4, 4–22 (1987). [CrossRef]
  3. R. M. May, “Simple Mathematical Models with Very Complicated Dynamics”, Nature (London) 261, 459–473 (1976). [CrossRef]
  4. M. Fang, G. Häusler, “Chaos and Cooperation in Nonlinear Pictorial Feedback Systems,” Proc. Soc. Photo-Opt. Instrum. Eng. 667, 214–219 (1986).
  5. J. R. Fienup, “Reconstruction of an Object from the Modulus of Its Fourier Transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]
  6. R. W. Gerchberg, W. O. Saxton, “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures,” Optik 35, 237–246 (1972).
  7. G. R. Ayers, J. C. Dainty, “Iterative Blind Deconvolution Method and Its Applications,” Opt. Lett. 13, 547–549 (1988). [CrossRef] [PubMed]
  8. L. M. Kani, J. C. Dainty, “Super Resolution Using the Gerchberg Algorithm,” Opt. Commun. 68, 11–17 (1988). [CrossRef]
  9. D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
  10. G. J. Dunning, E. Marom, Y. Owechko, B. H. Soffer, “All-Optical Associative Memory with Shift Invariance and Multiple-Image Recall,” Opt. Lett. 12, 346–351 (1987). [CrossRef] [PubMed]
  11. K. Nakano, “A Model of Associative Memory,” IEEE Trans. Syst. Man Cybern. SMC-2, 380–388 (1972). [CrossRef]
  12. S. I. Amari, “Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements,” IEEE Trans. Comput. C-21, 1197–1206 (1972). [CrossRef]
  13. S. I. Amari, “Neural Theory of Association and Concept Formation,” Biol. Cybern. 26, 175–186 (1977). [CrossRef] [PubMed]
  14. J. Anderson, J. Silverstein, S. Ritz, R. Jones, “Distinction Features, Categorial Perception and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413–451 (1977). [CrossRef]
  15. J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Nat. Acad. Sci. USA 79, 2554–2558 (1982). [CrossRef] [PubMed]

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