Statistical Computation Methods and Algorithms

  • Leonid Yaroslavsky


By definition, the distribution function P ( V ) of a random variable v is the probability that the random variable does not exceed the value V. The derivative of P ( V ) with respect to V
$$ p\left( v \right) = {\left. {\frac{{dP\left( V \right)}}{{dV}}} \right|_{V = v}} $$
is called the probability distribution density of the random variable v. Digital signals are characterized by discrete analogs of the distribution function and distribution density respectively — the relative share R ( m ) of the samples that do not exceed the given quantized value q, and the rate h ( q ) of the samples having the value q. The latter characteristic is referred to as signal distribution histogram,the former one as cumulative distribution histogram.


Power Spectrum Impulse Noise Speckle Noise Digital Holography Speckle Contrast 
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  1. 1.
    P. J. Huber, Robust Statistics, John Wiley and Sons, N.Y., 1981Google Scholar
  2. 2.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Receipes in C. The Art of Scientific Computing, Second Edition, Cambridge University Press, 1995Google Scholar
  3. 3.
    L. Yaroslaysky, M. Eden, Fundamentals of Digital Optics, Birkhauser, Boston, 1995Google Scholar
  4. 4.
    L. B. Lesern, P. M. Hirsch, J. A. Jordan, Kinoform, IBM Journ. Res. Dev., 13, 150, 1969Google Scholar
  5. 5.
    L. P. Yaroslayskii, N. S. Merzlyakov, Methods of Digital Holography, Consultant Bureau, N.Y., 1980Google Scholar
  6. 6.
    N. C. Gallagher, B. Liu, Method for Computing Kinoforms that Reduces Image Reconstruction Error, Applied Optics, v. 12, No. 10, Oct. 1973, p. 2328ADSCrossRefGoogle Scholar
  7. 7.
    Goodman, J.W.,. Statistical Properties of Laser Speckle Patterns In Laser Speckle and Related Phenomena, J.C. Dainty, ed. Springer Verlag, Berlin, 1975Google Scholar
  8. 8.
    L. Yaroslaysky, A. Shefler, Statistical characterization of speckle noise in coherent imaging systems, in: Optical Measurement Systems for Industrial Inspection III, SPIE’s Int. Symposium on Optical Metrology, 23–25 June 2003, Munich, Germany, W. Osten, K. Creath, M. Kujawinska, Eds., SPIE v. 5144, pp. 175–182Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Leonid Yaroslavsky
    • 1
  1. 1.Tel Aviv UniversityIsrael

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