The two entropy expressions, logB 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 logB 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.
© 1978 Optical Society of America
Ryoichi Kikuchi and B. H. Soffer, "Maximum entropy image restoration. I. The entropy expression," J. Opt. Soc. Am. 67, 1656-1665 (1977)