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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 64, Iss. 11 — Nov. 1, 1974
  • pp: 1498–1502

Degrees of freedom, and eigenfunctions, for the noisy image

M. Bendinelli, A. Consortini, L. Ronchi, and B. Roy Frieden  »View Author Affiliations


JOSA, Vol. 64, Issue 11, pp. 1498-1502 (1974)
http://dx.doi.org/10.1364/JOSA.64.001498


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Abstract

An eigenvalue analysis of the noise-prone image leads to (a) an analysis of the eigenfunctions and eigenvalues of the sin<sup>2</sup>(<i>x</i>)/<i>x</i><sup>2</sup> kernel; and (b) an expression relating an effective number <i>N</i><sub>eff</sub> of degrees of freedom directly to the signal-to-noise ratio σ<sub>0</sub>/σ<sub><i>v</i></sub>. The latter are the variances of object and noise, respectively. For the particular case of incoherent, diffraction-limited imagery, <i>N</i><sub>eff</sub> is found to be reduced from its noise-free value, the Shannon number, by the factor (1-σ<sub><i>v</i></sub>/σ<sub>0</sub>). A maximum number <i>N</i><sub>max</sub> of degrees of freedom is also defined. Comparing one-dimensional objects illuminated alternatively by coherent and incoherent light, we find they have the same number <i>N</i><sub>max</sub> of degrees of freedom. However, for the corresponding two-dimensional case, the incoherent value for <i>N</i><sub>max</sub> is double that of the coherent value.

Citation
M. Bendinelli, A. Consortini, L. Ronchi, and B. Roy Frieden, "Degrees of freedom, and eigenfunctions, for the noisy image," J. Opt. Soc. Am. 64, 1498-1502 (1974)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-64-11-1498


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References

  1. G. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955).
  2. G. Toraldo di Francia, Trans. IRE AP-4, 473 (1956).
  3. C. K. Rushforth and R. W. Harris, J. Opt. Soc. Am. 58, 539 (1968).
  4. G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).
  5. B. R. Frieden, in Progress in Optics, IX, edited by E. Wolf, (North-Holland, Amsterdam, 1971), p. 311.
  6. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  7. F. Riesz and B. S. Nagy, Functional Analysis (Fredelich Angars, New York, 1965).
  8. A. Fedotowsky, thesis (Laval University, Canada) (1972).
  9. F. Gori and G. Guattari, Opt. Commun. 7, 163 (1973).
  10. H. J. Landau, Acta Math. 117, 37 (1967).
  11. R. L. Sanderson and W. Streifer, Appl. Opt. 8, 131 (1969).
  12. A. Consortini and F. Pasqualetti, Opt. Acta 20, 793 (1973).
  13. B. R. Frieden, J. Opt. Soc. Am. 62, 511 (1972).

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