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The Internal Linear Combination (ILC) method has been extensively used toextract the cosmic microwave background (CMB) anisotropy map from foregroundcontaminated multi-frequency maps. However, the performance of simple ILC islimited and can be significantly improved by heavily constraint equations,dubbed cILC. The standard ILC and cILC works on the spin-0 field. Recently, ageneralized version of ILC is developed to estimate polarization maps in whichthe quantity $Q \pm iU$ is combined at multiple frequencies using complexcoefficients called Polarization ILC (PILC). A statistical moment expansionmethod has recently been developed for high precision modelling of the Galacticforegrounds. This paper develops a semi-blind component separation methodcombining the moment approach of foreground modelling with a generalizedversion of the PILC method for heavily constraint equations. The algorithm isdeveloped in pixel space and performs for a spin-2 field. We employ thiscomponent separation technique in simultaneous estimation of Stokes $Q$, $U$maps of the thermal dust at 353 GHz and synchrotron at 30 GHz over 78 % of thesky. We demonstrate the performance of the method on three sets of absolutelycalibrated simulated maps at WMAP and planck frequencies with varyingforeground models.

A new approach of estimating the Galactic thermal dust and synchrotron polarized emission template in the microwave bands