De-Confusing blended field images using graphs and bayesian priors

We present a new technique for overcoming confusion noise in deep far-infrared \Herschel space telescope images making use of prior information from shorter $λ<2$\micron wavelengths. For the deepest images obtained by \Herschels, the flux limit due to source confusion is about a factor of three brighter than the flux limit due to instrumental noise and (smooth) sky background. We have investigated the possibility of de-confusing simulated \Herschel PACS-160\micron images by using strong Bayesian priors on the positions and weak priors on the flux of sources. We find the blended sources and group them together and simultaneously fit their fluxes. We derive the posterior probability distribution function of fluxes subject to these priors through Monte Carlo Markov Chain (MCMC) sampling by fitting the image. Assuming we can predict FIR flux of sources based on ultraviolet-optical part of their SEDs to within an order of magnitude, the simulations show that we can obtain reliable fluxes and uncertainties at least a factor of three fainter than the confusion noise limit of $3σ_{c} $=2.7 mJy in our simulated PACS-160 image. This technique could in principle be used to mitigate the effects of source confusion in any situation where one has prior information of positions and plausible fluxes of blended sources. For \Herschel, application of this technique will improve our ability to constrain the dust content in normal galaxies at high redshift.