Bayesian analysis of signals from closely-spaced objects

Bayesian probability theory is applied to the problem of the resolution of closely-spaced objects. The conditions assumed are: point sources, observed through a known smearing function (i.e., point-spread function). For this demonstration we use a Gaussian smearing function so that we can obtain analytic results; however, we present graphical results for both the Gaussian and the Airy smearing functions. The generalizations to arbitrary smearing functions may be found in other works by Bretthorst.1,2,3 The results obtained for one and two point sources indicate explicitly the dependence of resolution on signal-to-noise and on the smearing function.