Bayesian cross-entropy reconstruction of complex images

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Abstract
Bajkova's generalized maximum entropy method for reconstruction of complex signals is further generalized through the use of Kullback–Leibler cross entropy. This permits a priori information in the form of bias functions to be inserted into the algorithm, with resulting benefits to reconstruction quality. Also, the cross-entropy term is imbedded within an overall maximum a posteriori probability approach that includes a noise-rejection term. A further modification is transformation of the large two-dimensional problem arising from modest-sized two-dimensional images into a sequence of one-dimensional problems. Finally the added operation of three-point median window filtration of each intermediary one-dimensional output is shown to suppress edge-top overshoots while augmenting edge gradients. Applications to simulated complex images are shown.

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