Future Cosmic Microwave Background (CMB) experiments will provide high resolution sky maps covering a wide range of frequencies. In addition to the cosmological CMB signal those maps will contain instrumental noise and contributions from Galactic and extragalactic foregrounds. The denoising of these maps as well as the separation of the different components from the CMB signal are the most challenging problems for CMB cosmology. The final goal would be to reconstruct CMB maps trying not to loose structural details as well as to recover the radiation power spectrum with the minimum error. In a first approach to these problems we present in this paper a denoising technique based on wavelets. Previously there have been other works based in the use of Wiener filter (Tegmark & Efstathiou ) and Maximum Entropy Methods (Hobson et al. [1998,1999]). The use of denoising methods based on wavelets have certain advantages as providing information of the contribution of different scales, being computationally faster (0(N)) and not requiring iterative processes. The analysis of discrete 2-dimensional images with wavelets can be performed following different approaches. The two computationally faster algorithms are the ones based on Multiresolution analysis (Mallat ) and on 2D wavelet analysis (Lemarié & Meyer ), using tensor products of one dimensional wavelets. A study of denoising of CMB maps using the former method has been presented in Sanz et al. (). This method is based on a single scale and three "details'' at each resolution level. The 2-D wavelet method used in this work is based on two scales, providing therefore more information on different resolutions (defined by the product of the two scales) than the Multiresolution one. Moreover this technique is adapted to separable wavelets. On the other hand, an analysis of denoising using spherical wavelets has been recently carried out by Tenorio et al. ().
The paper is organized as follows. In Sect. 2 we present some basic ideas about the continuous 2D wavelet transform. We apply 2-D wavelets to the analysis of discrete 2D CMB anisotropy maps of small sky patches in Sect. 3 and the conclusions are presented in Sect. 4.
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