Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which producesmaps which are optimal in the Bayesian sense of maximum posterior probabilitydensity, given certain prior assumptions. It is similar to maximum entropytechniques, but with an exact accounting of the multiplicity instead of theusual approximation involving Stirling's formula. It also incorporates an Occamfactor, automatically limiting the effective amount of detail in the map tothat justified by the data. We use Gibbs sampling to determine, to any desireddegree of accuracy, the multi-dimensional posterior density distribution. Fromthis we can construct a mean posterior map and other measures of the posteriordensity, including confidence limits on any well-defined function of theposterior map.