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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 sin2(x)/x2 kernel; and (b) an expression relating an effective number Neff of degrees of freedom directly to the signal-to-noise ratio σ0v. The latter are the variances of object and noise, respectively. For the particular case of incoherent, diffraction-limited imagery, Neff is found to be reduced from its noise-free value, the Shannon number, by the factor (1-σv0). A maximum number Nmax 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 Nmax of degrees of freedom. However, for the corresponding two-dimensional case, the incoherent value for Nmax 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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