Analysis of CMB maps with 2D Wavelets

We consider the 2D wavelet transform with two scales to study sky maps of temperature anisotropies in the cosmic microwave background radiation (CMB). We apply this technique to simulated maps of small sky patches of size 12.8◦ × 12.8◦ and 1.5′ × 1.5′ pixels. The relation to the standard approach, based on the C′ ls, is established through the introduction of the scalogram. We consider temperature fluctuations derived from standard, open and flat-Λ Cold Dark Matter (CDM) models. We analyze CMB anisotropies maps plus uncorrelated Gaussian noise (uniform and non-uniform) at different S/N levels. We explore in detail the denoising of such maps and compare the results with other techniques already proposed in the literature. Wavelet methods provide a good reconstruction of the image and power spectrum. Moreover, they are faster than previously proposed methods.