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

Abstract

Analysis and denoising of cosmic microwave background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12.8 × 12.8 deg2 maps, with the resolution resembling the experimental one expected 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 wavelet coefficients dominated by instrumental noise. CMB maps with a signal-to-noise ratio, S/N ∼ 1, are denoised with an error improvement factor between 3 and 5. Moreover, we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the Cℓs up to l ∼ 1500 with errors always below 20 per cent in cases with S/N ≥ 1.