Two‐dimensional maximum entropy reconstruction of radio brightness

Abstract

This paper describes a procedure for maximum entropy reconstruction of two‐dimensional radio brightness maps from noisy interferometer measurements. The method defines a map that obeys the nonnegativity constraint and is, in a sense, the smoothest of all brightness distributions that agree with the visibility measurements within the errors of observation. This approach acknowledges the fact that signal‐to‐noise considerations have a strong influence on useful resolution; fine structure appears only to the extent justified by measurement accuracy. Iterative computing is needed to find the maximum entropy image. It is shown that the primary computational burden of maximum entropy reconstruction involves calculations that are efficiently performed by fast Fourier transform techniques. Different techniques are used depending on whether visibility data are irregularly distributed in the u,v plane or interpolated onto a rectangular lattice prior to reconstruction. The efficiency of the fast Fourier transform provides a tremendous computational advantage with the result that maximum entropy reconstruction on a moderately large grid (64×64) is practicable at reasonable cost. Several comparative examples are shown, and some of the limitations of the present theory of maximum entropy imaging are identified.