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

In this paper we analyze the maximum entropy image deconvolution. We show that given the Lagrange multiplier a closed form can be obtained for the image parameters. Using this solution we are able to provide better understanding of some of the known behavior of the maximum entropy algorithm. The solution also yields a very efficient implementation of the maximum entropy deconvolution technique used in the AIPS package. It requires the computation of a single dirty image and inversion of an elementary function per pixel.