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 N_eff of degrees of freedom directly to the signal-to-noise ratio σ₀/σ_v. The latter are the variances of object and noise, respectively. For the particular case of incoherent, diffraction-limited imagery, N_eff is found to be reduced from its noise-free value, the Shannon number, by the factor (1 − σ_v/σ₀). A maximum number N_max 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 N_max of degrees of freedom. However, for the corresponding two-dimensional case, the incoherent value for N_max is double that of the coherent value.

© 1974 Optical Society of America

A priori information and the degrees of freedom of noisy images

Bahaa Saleh
J. Opt. Soc. Am. 67(1) 71-76 (1977)

Degrees of freedom of images from point-like-element pupils

F. Gori and G. Guattari
J. Opt. Soc. Am. 64(4) 453-458 (1974)

Degrees of Freedom of an Image

G. Toraldo di Francia
J. Opt. Soc. Am. 59(7) 799-804 (1969)

Effects of Coherence on the Degrees of Freedom of an Image

F. Gori and G. Guattari
J. Opt. Soc. Am. 61(1) 36-39 (1971)

Integral equations for incoherent imagery

F. Gori
J. Opt. Soc. Am. 64(9) 1237-1243 (1974)