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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 n¯ over an ensemble, the above two criteria remain the same (with n replaced by n¯), and in addition for the z = 1 case the logB expression, used in ME spectral power estimation, is derived for n¯⪢z=1.
Kikuchi et al. (1977) studied this question.