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White-noise analysis in visual neuroscience

Published online by Cambridge University Press:  02 June 2009

Hiroko M. Sakai ,
Naka Ken-Ichi  and
Michael J. Korenberg
Naka Ken-Ichi
Affiliation:
National Institute for Basic Biology, Okazaki, Japan
Michael J. Korenberg
Affiliation:
Department of Electrical Engineering, Queens University, Kingston, Ontario
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Abstract

In 1827, plant biologist Robert Brown discovered what is known as Brownian motion, a class of chaos. Formal derivative of Brownian motion is Gaussian white-noise. In 1938, Norbert Wiener proposed to use the Gaussian white-noise as an input probe to identify a system by a series of orthogonal functionals known as the Wiener G-functionals.

White-noise analysis is uniquely suited for studying the response dynamics of retinal neurons because (1) white-noise light stimulus is a modulation around a mean luminance, as are the natural photic inputs, and it is a highly efficient input; and (2) the analysis defines the response dynamics and can be extended to spike trains, the final output of the retina. Demonstrated here are typical examples and results from applications of white-noise analysis to a visual system.

Keywords

RetinaPiecewise linearizationStatic nonlinearitySpike generationWiener kernel
Type
Research Article
Information
Visual Neuroscience , Volume 1 , Issue 3 , May 1988 , pp. 287 - 296
Copyright
Copyright © Cambridge University Press 1988

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References

Bruce, C., Desimore, R. & Gross, C.G. (1981). Visual properties of neurons in a polysensory area in superior temporal sulcus of the Macaque. Journal of Neurophysiology (Bethesda, MD), 46, 369–384.Google Scholar
Chappell, R.L., Naka, K.-I. & Sakuranaga, M. (1985). Dynamics of turtle horizontal cells. Journal of General Physiology (New York), 86, 423–453.Google Scholar
Daly, S.J. & Normann, R.A. (1985). Temporal information processing in cones: effects of light adaptation on temporal summation and modulation. Vision Research (Oxford), 25, 1197–1206.CrossRefGoogle ScholarPubMed
de Boer, E. & Kuyper, P. (1968). Triggered correlation. IEEE Transactions on Biomedical Engineering (New York), 15, 169–179.CrossRefGoogle ScholarPubMed
Fréchet, M. (1910). Sur les fonctionelles continues. Annales Scientifiques de I'Ecole Normale Superieure, 27, 193–216.CrossRefGoogle Scholar
French, A.S. & Butz, E.G. (1973). Measuring the Wiener kernels of a nonlinear system using the fast Fourier transform algorithm. International Journal of Control, 17, 529–539.CrossRefGoogle Scholar
Hida, E. & Naka, K.-I. (1982). Spatio-temporal receptive field as revealed by spatio-temporal random noise. Zeitschrift für Naturforschung, 37C, 1048–1049.CrossRefGoogle Scholar
Hida, T. (1980). Brownian Motion. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Hunter, I.W. (1985). Frog muscle fiber dynamic stiffness determined using nonlinear system identification techniques. Biophysical Journal (New York), 47, 287.Google Scholar
Korenberg, M.J. (1973). Identification of biological cascades of linear and static nonlinear systems. Proceedings of the 16th Midwest Symposium Circuit Theory, 18–2, 1–9.Google Scholar
Korenberg, M.J. & Hunter, I.W. (1986). The identification of nonlinear biological systems: LNL cascade models. Biological Cybernetics (Berlin), 55, 125–134.CrossRefGoogle ScholarPubMed
Korenberg, M.J. (1988). Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm. Annals of Biomedical Engineering (New York), 16, 123–142.CrossRefGoogle ScholarPubMed
Korenberg, M.J., Bruder, S.B. & McIlroy, P.J. (1988 a). Exact orthogonal kernel estimation from finite data records: extending Wiener's identification of nonlinear systems. Annals of Biomedical Engineering (New York), 16, 201–214.Google Scholar
Korenberg, M.J., French, A.S. & Voo, S.K.L. (1988 b). White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches. Biological Cybernetics (Berlin), 58, 313–320.Google Scholar
Lee, Y.W. & Schetzen, M. (1965). Measurement of the Wiener kernels of a non-linear system by cross-correlation. International Journal of Control, 2, 237–254.CrossRefGoogle Scholar
Marmarelis, P.Z. & Naka, K.-I. (1973 a). Nonlinear analysis and synthesis of receptive-field responses in the catfish retina. I. horizontal cell—ganglion cell chain. Journal of Neurophysiology (Bethesda, MD), 36, 605–618.Google Scholar
Marmarelis, P.Z. & Naka, K.-I. (1973 b). Nonlinear analysis and synthesis of receptive-field responses in the catfish retina. III. Two-input white-noise analysis. Journal of Neurophysiology (Bethesda, MD), 36, 634–648.Google Scholar
Marmarelis, P.Z. & Marmarelis, V.Z. (1978). Analysis of Physiological Systems: The White-noise Approach. New York: Plenum Press.CrossRefGoogle Scholar
Mizuno, M., Imai, S., Tsukada, M., Hida, E. & Naka, K.-I. (1985). A micro-computer system for spatio-temporal visual receptive field analysis. IEEE Transactions on Biomedical Engineering (New York), 32, 56–59.CrossRefGoogle Scholar
Naka, K.I. & Rushton, W.A.H. (1966). S-potentials from colour units in the retina of fish (cyprinidae). Journal of Physiology (London), 185, 536–555.Google Scholar
Naka, K.-I., Marmarelis, P.Z. & Chan, R.Y. (1975). Morphological and functional identification of catfish retinal neurons. III. Functional identification. Journal of Neurophysiology (Bethesda, MD), 38, 92–131.Google Scholar
Naka, K.-I., Chan, R.Y. & Yasui, S. (1979). Adaptation in catfish retina. Journal of Neurophysiology (Bethesda, MD), 42, 441–454.CrossRefGoogle ScholarPubMed
Naka, K.-I., Itoh, M.-A & Chappell, R.L. (1987). Dynamics of turtle cones. Journal of General Physiology (New York), 89, 321–338.Google Scholar
Ogura, H. (1986). Estimation of Wiener kernels of a nonlinear system and fast algorithm using digital Laguerre filters. In Information Processing in Neuron Network: White-noise analysis, eds. Naka, K.-I. & Ando, Y.-I., pp. 14–62. NIBB (Okazaki, Japan).Google Scholar
Powers, R.I. & Arnett, D.W. (1981). Spatio-temporal cross-correlation analysis of catfish retinal neurons. Biological Cybernetics (Berlin), 41, 179–196.Google Scholar
Rugh, W.J. (1981). Nonlinear System Theory: The Volterra/Wiener Approach. Baltimore: The Johns Hopkins Univ Press.Google Scholar
Rushton, W.A.H. (1975). The Ferrier lecture. Visual adaptation. Proceedings of the Royal Society of London Biological Sciences, 162, 20–46.Google Scholar
Sakai, H.M. & Naka, K.-I. (1987 a). Signal transmission in the catfish retina. IV. Transmission to ganglion cell. Journal of Neurophysiology (Bethesda, MD), 56, 1307–1328.Google Scholar
Sakai, H.M. & Naka, K.-I. (1987 b). Signal transmission in the catfish retina. V. Sensitivity and Circuit. Journal of Neurophysiology (Bethesda, MD), 56, 1329–1350.CrossRefGoogle Scholar
Sakuranaga, M. & Naka, K.-I. (1985 a). Signal transmission in the catfish retina. I. Transmission in the outer retina. Journal of Neurophysiology (Bethesda, MD), 53, 373–389.CrossRefGoogle ScholarPubMed
Sakuranaga, M. & Naka, K.-I. (1985 b). Signal transmission in the catfish retina. II. Transmission to type-N cell. Journal of Neurophysiology (Bethesda, MD), 53, 390–410.CrossRefGoogle ScholarPubMed
Sakuranaga, M. & Naka, K.-I. (1985 c). Signal transmission in the catfish retina. III. Transmission to type-C cell. Journal of Neurophysiology (Bethesda, MD), 53, 411–428.CrossRefGoogle ScholarPubMed
Sakuranaga, M., Sato, N., Hida, E. & Naka, K.-I. (1986). Nonlinear analysis: Mathematical theory and biological applications. Critical Reviews in Biomedical Engineering, 14, 127–184.Google ScholarPubMed
Sakuranaga, M., Ando, Y.-I. & Naka, K.-I. (1987). Dynamics of ganglion-cell response in the catfish and frog retinas. Journal of General Physiology (New York), 90, 229–259.CrossRefGoogle ScholarPubMed
Schellart, N.A.M. & Spekreuse, H. (1972). Dynamic characteristics of retinal ganglion cell responses in goldfish. Journal of General Physiology (New York), 59, 1–21.CrossRefGoogle ScholarPubMed
Schetzen, M. (1980). The Volterra and Wiener Theory of Nonlinear Systems. New York: John Wiley & Sons.Google Scholar
Spekreuse, H., Estevez, O. & Reits, D. (1977). Visual evoked potentials and the physiological analysis of visual processes in man. In Visual Evoked Potentials in Man, ed. Desmedt, J., pp. 16–89. Oxford; Clarendon Press.Google Scholar
Tranchina, D., Gordon, J., Shapley, R. & Toyoda, J.-I. (1981). Linear information processing in the retina: a study of horizontal cell response. Proceedings of the National Academy of Sciences of the United States of America (Washington), 78, 6540–6542.Google Scholar
Tranchina, D., Gordon, J. & Shapley, R. (1983). Spatial and temporal properties of luminosity horizontal cells in the turtle retina. Journal of General Physiology (New York), 82, 573–598.CrossRefGoogle ScholarPubMed
Tranchina, D., Gordon, J. & Shapley, R. (1984). Retinal light adaptation–evidence for a feedback mechanism. Nature, 310, 314–316.CrossRefGoogle ScholarPubMed
Victor, J.D. & Shapley, R.M. (1979). The nonlinear pathway of Y ganglion cells in the cat retina. Journal of General Physiology (New York), 74, 671–689.Google Scholar
Volterra, V. (1913). Leçons sur les Fonctions De Lignes. Paris: Gauthier-Villars.Google Scholar
Volterra, V. (1959). Theory of Functionals and of Integral and Integro-differential Equations. New York: Dover Publications, Inc.Google Scholar
Watanabe, A. (1986). An application of the Karhunen-Loeve expansion to measurement of the Volterra kernels. In Information Processing in Neuron Network: White-noise Analysis, eds. Naka, K.-l. & Ando, Y.-I., pp. 91–102. NIBB (Okazaki, Japan).Google Scholar
Wiener, N. (1938). The homogenous chaos. American Journal of Mathematics, 60, 897–936.CrossRefGoogle Scholar
Wiener, N. (1958). Nonlinear Problems in Random Theory. Wiley: New York.Google Scholar