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In this paper we analyze the maximum entropy image deconvolution. We showthat given the Lagrange multiplier a closed form can be obtained for the imageparameters. Using this solution we are able to provide better understanding ofsome of the known behavior of the maximum entropy algorithm. The solution alsoyields a very efficient implementation of the maximum entropy deconvolutiontechnique used in the AIPS package. It requires the computation of a singledirty image and inversion of an elementary function per pixel.

Closed form solution of the maximum entropy equations with application to fast radio astronomical image formation