Wavelets applied to cosmic microwave background maps: a multiresolution analysis for denoising

Analysis and denoising of cosmic microwave background (CMB) maps are perfor med using wavelet multiresolution techniques. The method is tested on 12.8 x 12.8 deg(2) maps, with the resolution resembling the experimental one exp ected for future high-resolution space observations. Semi-analytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard cold dark matter (CDM) model. Denoising of simulated maps is carried out by removal of wave let coefficients dominated by instrumental noise. CMB maps with a signal-to -noise ratio, S/N similar to 1, are denoised with an error improvement fact or between 3 and 5. Moreover, we have also tested how well the CMB temperat ure power spectrum is recovered after denoising, We are able to reconstruct the C(l)s up to l similar to 1500 with errors always. below 20 per cent in cases with S/N greater than or equal to 1.