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ABSTRACT  The cosmic microwave background (CMB) radiation data obtained by different experiments contain, besides the desired signal, a superposition of microwave sky contributions. Using a wavelet decomposition on the sphere, we present a fast and robust method to recover the CMB signal from microwave maps. We present an application to the  Wilkinson Microwave Anisotropy Probe  ( WMAP ) polarization data, which shows its good performance, particularly in very polluted regions of the sky. The applied wavelet has the advantages that it requires little computational time in its calculations, it is adapted to the  healpix  pixelization scheme and it offers the possibility of multiresolution 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 χ 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  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  is computed at high and low resolutions, and a cross‐power spectrum  is also calculated from the foreground reduced maps of temperature given by  WMAP  and our cleaned maps of polarization at high resolution. These spectra are consistent with the power spectra supplied by the  WMAP  team. We detect the E‐mode acoustic peak at ℓ∼ 400, as predicted by the standard ΛCDM model. The B‐mode power spectrum  is compatible with zero.

Multiresolution internal template cleaning: an application to the Wilkinson Microwave Anisotropy Probe 7‐yr polarization data