Determination of X-Ray Transient Source Positions By Bayesian Analysis of Coded Aperture Data

We present a new method of transient point source deconvolution for coded-aperture X-Ray detectors. Our method is based upon the calculation of the likelihood function and its interpretation as a probability density for the transient source position by an application of Bayes' Theorem. The method obtains point estimates of source positions by finding the maximum of this probability density, and interval estimates of prescribed probability by choosing suitable contours of constant probability density. We give the results of simulations that we performed to test the method. We also derive approximate analytic expressions for the predicted performance of the method. These estimates underline the intuitively plausible properties of the method and provide a sound quantitative basis for the design of coded-aperture systems.