Multi-resolution internal template cleaning: An application to the   Wilkinson Microwave Anisotropy Probe 7-yr polarization data
  Cosmic microwave background (CMB) radiation data obtained by different experiments contain, besides the desired signal, a superposition of microwave sky contributions. We present a fast and robust method, using a wavelet decomposition on the sphere, to recover the CMB signal from microwave maps. An application to \textit{WMAP} polarization data is presented, showing its good performance particularly in very polluted regions of the sky. The applied wavelet has the advantages of requiring little computational time in its calculations, being adapted to the \textit{HEALPix} pixelization scheme, and offering the possibility of multi-resolution analysis. The decomposition is implemented as part of a fully internal template fitting method, minimizing the variance of the resulting map at each scale. Using a $\chi^2$ characterization of the noise, we find that the residuals of the cleaned maps are compatible with those expected from the instrumental noise. The maps are also comparable to those obtained from the \textit{WMAP} team, but in our case we do not make use of external data sets. In addition, at low resolution, our cleaned maps present a lower level of noise. The E-mode power spectrum $C_{\ell}^{EE}$ is computed at high and low resolution; and a cross power spectrum $C_{\ell}^{TE}$ is also calculated from the foreground reduced maps of temperature given by \textit{WMAP} and our cleaned maps of polarization at high resolution. These spectra are consistent with the power spectra supplied by the \textit{WMAP} team. We detect the E-mode acoustic peak at $\ell \sim 400$, as predicted by the standard $\Lambda CDM$ model. The B-mode power spectrum $C_{\ell}^{BB}$ is compatible with zero. 
R. Fern\'andez-Cobos, P. Vielva, R.B. Barreiro, E.   Mart\'inez-Gonz\'alez
astro-ph.CO