Analysis and denoising of Cosmic Microwave Background (CMB) maps areperformed using wavelet multiresolution techniques. The method is tested on$12^{\circ}.8\times 12^{\circ}.8$ maps with resolution resembling theexperimental one expected for future high resolution space observations.Semianalytic formulae of the variance of wavelet coefficients are given for theHaar and Mexican Hat wavelet bases. Results are presented for the standard ColdDark Matter (CDM) model. Denoising of simulated maps is carried out by removalof wavelet coefficients dominated by instrumental noise. CMB maps with asignal-to-noise, $S/N \sim 1$, are denoised with an error improvement factorbetween 3 and 5. Moreover we have also tested how well the CMB temperaturepower spectrum is recovered after denoising. We are able to reconstruct the$C_{\ell}$'s up to $l\sim 1500$ with errors always below $20% $ in cases with$S/N \ge 1$.
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机译：使用小波多分辨率技术对宇宙微波背景图（CMB）进行分析和去噪。该方法在$ 12 ^ {\ circ} .8 \乘以12 ^ {\ circ} .8 $地图上进行了测试，其分辨率与未来高分辨率空间观测所期望的实验相似。给出了Haar的小波系数方差的解析公式。和墨西哥帽小波基。给出了标准ColdDark Matter（CDM）模型的结果。通过去除以仪器噪声为主的小波系数对模拟图进行去噪。具有信噪比的CMB图$ S / N \ sim 1 $被去噪，误差改善系数在3到5之间。此外，我们还测试了去噪后CMB温度功率谱的恢复程度。在$ S / N \ ge 1 $的情况下，我们能够重建$ C _ {\ ell} $直至$ l \ sim 1500 $，错误始终低于$ 20％$。
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