Abstract

The two entropy expressions, log B and −B logB (where B is the local brightness of the object or its spatial spectral power) used in maximum entropy (ME) image restoration, are derived as limiting cases of a general entropy formula. The brightness B is represented by the n photons emitted from a small unit area of the object and imaged in the receiver. These n photons can be distributed over z degrees of freedom in q(n,z) different ways calculated by the Bose-Einstein statistics. The entropy to be maximized is interpreted, as in the original definition of entropy by Boltzmann and Planck, as logq(n,z). This entropy expression reduces to log B and −B logB in the limits of $n⪢z>1$ and $n⪡z$, respectively. When n is interpreted as an average $\overline{n}$ over an ensemble, the above two criteria remain the same (with n replaced by $\overline{n}$), and in addition for the z = 1 case the logB expression, used in ME spectral power estimation, is derived for $\overline{n}⪢z=1$.

© 1977 Optical Society of America

A deterministic analysis of the maximum entropy image restoration method and of some related methods

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J. Opt. Soc. Am. 67(9) 1154-1159 (1977)

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Restoring with maximum entropy. III. Poisson sources and backgrounds

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Restoring with Maximum Entropy, II: Superresolution of Photographs of Diffraction-Blurred Impulses*

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