We propose a new detection technique in the plane based on an isotropic wavelet family .
This family is naturally constructed as an extension of the Gaussian-Mexican Hat Wavelet pair and for that reason we call it the Mexican Hat Wavelet Family ( MHWF ) .
We show the performance of these wavelets when dealing with the detection of extragalactic point sources in cosmic microwave background ( CMB ) maps : a very important issue within the most general problem of the component separation of the microwave sky .
Specifically , flat two-dimensional simulations of the microwave sky comprising all astrophysical components plus instrumental noise have been analyzed for the channels at 30 , 44 and 70 GHz of the forthcoming ESA ’ s Planck mission Low Frequency Instrument ( LFI ) .
We adopt up-to-date cosmological evolution models of extragalactic sources able to fit well the new data on high-frequency radio surveys and we discuss our current results on point source detection by comparing them with those obtained using the Mexican Hat Wavelet ( MHW ) technique , which has been already proven a suitable tool for detecting point sources .
By assuming a 5 % reliability level , the first new members of the MHWF , at their “ optimal scale ” , provide three point source catalogues on half of the sky ( at galactic latitude |b| > 30 ^ { \circ } ) at 30 , 44 and 70 GHz of 639 , 387 and 340 extragalactic sources , respectively .
The corresponding flux detection limits are 0.38 , 0.45 and 0.47 Jy .
By using the same simulated sky patches and at the same frequencies as before , the MHW at its optimal scale provides 543 , 322 and 311 sources with flux detection limits of 0.44 , 0.51 and 0.50 Jy , respectively ( 5 % reliability level ) .
These results show a clear improvement when we use the new members of the MHWF and , in particular , the MHW2 with respect to the MHW .