Lensing map reconstruction from 02.00 sims w/ and w/o foreground+inhomogeneous noise

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Septemper 26, 2018 (Toshiya Namikawa posted)


In this posting, I show some results of the reconstruction of the CMB lensing kappa map from the signal only or signal+noise+foreground simulations. I used two quadratic estimators, TT and EB, and show that the reconstructed kappa map looks agree with the input kappa map even after including the noise and foreground. However, the reconstruction noise becomes larger at smaller scales of the reconstructed kappa. This could affect the delensing efficiency.


Following [1], I use the following simulation data set:

- The high res masked lensed-LCDM single frequency map


- The high res masked lensed-LCDM + noise + foreground single frequency map


- Relative hits mask


- The true input phi map

 /project/projectdirs/cmb/data/generic/cmb/ffp10/mc/scalar/ffp10_unlensed_scl_cmb_000_tebplm_mc_0000.fits (4th binary table)

- The input lensed-LCDM angular power spectra (TT,TE,EE,BB)


(Note that what I actually use is the mirror of the above data at Odyssey.)

Fig.1 shows the angular power spectra of the CMB alms.

Fig cmbcl TT.jpg Fig cmbcl EE.jpg Fig cmbcl BB.jpg

Fgi.1: The CMB temperature, EE, and BB power spectra from the signal only or signal+noise+foreground sims.


The method of the lensing reconstruction is very similar to that of BICEP2/Keck Array Results Paper VIII [[2]] (hereafter BKVIII), except the curved sky analysis.

I first compute the diagonal filtering to be applied to the CMB harmonic coefficients (see text around Eq.(17) of BKVIII). The T, E and B at 500<L<3000 are used for the reconstruction. The unnormalized kappa estimator is then computed (e.g., for EB, fullsky counterpart of Eq.(19) of BKVIII). The analytic fullsky normalization is computed and multiplied to the unnormalized estimator. The mean field is then subtracted. The reconstructed kappa map is finally cross-correlated with the input kappa map. The wiener-filtered phi is also computed.


Fig kmap input.jpg Fig kmap recon.jpg

Fig.2: Example of the input kappa map after applying the mask. The kappa multipole at 50<L<200 is included in the fluctuations. The right panel is the same as the left panel but for the reconstructed kappa map using EB estimator from signal+noise+foreground simulation.

Fig kk TT.png Fig kk EB.png

Fig.3: The cross spectrum between input and reconstructed kappa (TT or EB estimator).

Fig vkk TT.png Fig vkk EB.png

Fig.4: The 1 sigma error of the reconstructed kappa auto spectrum (TT or EB estimator).


The input/reconstructed kappa map is currently located at


The file format is the fortran binary file. An example of reading the files (and showing the kappa map) is written in showkmap.py. For delensing study, I also put the wiener-filtered phi alms at


They are saved as fits files.