A Bayesian Approach To Flux Correction In Extragalactic Source Detection

In this paper we address a very relevant problem in astronomy, the estimation of the intensity of a source, in our case far galaxies in astronomical images, embedded in additive noise and selected by their observed intensity. We use a Bayesian approach that takes into account the distribution in intensity of the galaxies, that can be well described in parametric way as a power law with an unknown slope. We find a joint maximum likelihood of the slope of the distribution and the fluxes of all the galaxies detected in our images. We test the estimator with numerical simulations using the noise level of the 23 GHz channel of the NASA´s WMAP satellite. We find that with our method it is possible to determine the slope of the power law distribution with error lower than 5% and to correct the selection bias in the determination of the flux of the galaxies down to fluxes ~ 500 mJy