  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.
