An Alternating Maximization Of The Entropy/Likelihood Function For Image Reconstruction And Spectrum Estimation

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Abstract
We have shown that for the class of likelihood problems resulting from a complete-incomplete data specification in which the complete-data x are nonuniquely determined by the measured incomplete-data y via some many-to-one set of mappings y=h(x), the density which maximizes entropy is identical to the conditional density of the complete data given the incomplete data which would be derived via rules of conditional probability. It is precisely this identity between the maxent density and the conditional density which results in the fact that maximum-likelihood estimation problems may be solved via an iterative maximization of the sum of the entropy plus expected log-likelihood; the maximization is jointly with respect to the maxent density and the likelihood parameters. In this paper we demonstrate that for the problems of tomographic image reconstruction and spectrum estimation from finite data sets, this view results in the derivation of maximum-likelihood estimates of the image parameters and covariance parameters via an iterative maximization of the entropy function.

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