Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background maps

It is the aim of this paper to introduce the use of isotropic wavelets to d etect and determine the flux of point sources appearing in cosmic microwave background (CMB) maps. The most suitable wavelet to detect point sources f iltered with a Gaussian beam is the 'Mexican Hat'. An analytical expression of the wavelet coefficient obtained in the presence of a point source is p rovided and used in the detection and flux estimation methods presented. Fo r illustration the method is applied to two simulations (assuming Planck mi ssion characteristics) dominated by CMB (100 GHz) and dust (857 GHz), as th ese will be the two signals dominating at low and high frequencies respecti vely in the Planck channels. We are able to detect bright sources above 1.5 8 Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100 GHz ( 100 per cent of all), with errors in the flux estimation below 25 per cent. The main advantage of this method is that nothing has to be assumed about the underlying field, i.e. about the nature and properties of the signal pl us noise present in the maps. This is not the case in the detection method presented by Tegmark & Oliveira-Costa. Both methods are compared, producing similar results.