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

TL;DR

This paper derives a closed-form solution for maximum entropy image deconvolution, enhancing understanding and efficiency, especially for radio astronomical image formation, by simplifying computations to a single image and elementary function inversion per pixel.

Contribution

It provides a novel closed-form solution for maximum entropy equations, improving computational efficiency and understanding in radio astronomical image deconvolution.

Findings

Closed-form solution for maximum entropy equations derived.

Enhanced computational efficiency in deconvolution process.

Application to radio astronomical image formation demonstrated.

Abstract

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.