White Object Maximum Entropy

Suppose that prior knowledge is of the maximum-conviction form (20), where in addition all 

This corresponds to prior knowledge of an equal-energy white spectrum. Combining Eqs. (16) and (20) then yields 

Principle (17) now consists of just the Bose-Einstein degeneracy factor, exactly Kikuchi and Soffer s form (1977). Also, as these authors showed (see also Section IX.B), in the case (11a) of sparsely occupied df it becomes Jaynes s maximum-entropy form (39) (Jaynes, 1968). Hence, both the Kikuchi-Soffer and Jaynes estimators are special cases of the ML approach, corresponding to the prior knowledge that the unknown spectrum is equal-energy white with the highest conviction. 

This is a satisfying result. It has long been known that maximum entropy exerts a smoothing tendency on its estimate (Frieden, 1972). Now we see 

It has also been observed in past empirical work with maximum entropy that the outputs are quite accurate estimates of the true objects, often exhibiting resolution beyond (it would seem) the realm of possibility see Frieden (1972) or Wernecke and D Addario (1977). Now we can see why this should be true. These high-resolution estimates occurred only when the object consisted of isolated impulses against basically a flat background. That is, the object was essentially equal-energy white. In this case, as just discussed, the ML estimate is Kikuchi-Soffer or maximum entropy. These high-resolution outputs were therefore maximum likely as well  

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We can summarize this situation by the statement that the ML object obeys Jaynes s maximum-entropy principle when the white object definition (31) of maximum ignorance is used and when the object is of such low intensity that the df sites are mostly unoccupied. The latter situation is obeyed by weak astronomical objects such as planets in the visible and IR regions and the sun in the visible region (see Kikuchi and Softer, 1977). 

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