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Register a new userWavelets Applied to CMB Maps: a Multiresolution Analysis for Denoising
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Authors
J. L. Sanz
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Analysis and denoising of Cosmic Microwave Background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on $12^{circ}.8times 12^{circ}.8$ maps with resolution resembling the experimental one expected for future high resolution space observations. Semianalytic 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, $S/N sim 1$, 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 $C_{ell}$s up to $lsim 1500$ with errors always below $20% $ in cases with $S/N ge 1$.
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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 times 12.8 square degrees and 1.5 times 1.5 pixels. The relation to the standard approach, based on the cls is established through the introduction of the scalogram. We consider temperature fluctuations derived from standard, open and flat-Lambda CDM models. We analyze CMB anisotropies maps plus uncorrelated Gaussian noise (uniform and non-uniform) at idfferent 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.
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the {it Planck} collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. To study the randomness of the fields represented by each map we use the autocorrelation of the sequence of probe coefficients (which are just the full-sky Fourier coefficients $a_{ell,0}$ if the $z$ axis is taken in the probe direction). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We introduce a particular function on the sphere (called the emph{AC discrepancy}) that accentuates the departure from Gaussianity and isotropy. We find that for some of the maps, there are many directions for which the departures are significant, especially near the galactic plane. We also study the effect of varying the highest multipole used to calculate the AC discrepancy from the initial value of $1500$ to $2500$. In the case of Commander 2015, the AC discrepancy now exhibits antipodal blobs well away from the galactic plane. Finally, we look briefly at the non-inpainted Planck maps, for which the computed AC discrepancy maps have a very different character, with features that are global rather than local. For the particular case of the non-inpainted 2018 texttt{SEVEM} map (which has visible equatorial pollution), we model with partial success the observed behaviour by an isotropic Gaussian random field added to a non-random needlet-like structure located near the galactic centre.
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