Estimation of Full Sky CMB Angular Power Spectrum from High Resolution
  Partial Sky CMB Map Using Artificial Neural Network
  Reliable extraction of cosmological information from observed cosmic
microwave background (CMB) maps requires accurate removal of foreground
components. Since some regions of the sky are inevitably contaminated by strong
foreground signals, it may be desired to excise such strongly contaminated
regions even after a foreground subtraction has been performed. We employ an
artificial neural network (ANN) to predict the full sky CMB angular power
spectrum from the partial sky spectrum obtained from masked CMB anisotropy map,
at a high pixel resolution. We use a simple ANN with one hidden layer
containing $895$ neurons. Using $1.2 \times 10^{5}$ training samples of full
sky and corresponding partial sky spectra at Healpix pixel resolution parameter
$N_{side} = 256$, we show that predicted spectrum by our ANN agrees well with
the target spectrum at each realization for the multipole range $2 \leq l \leq
512$. The predicted spectra are statistically unbiased and they preserve the
cosmic variance accurately. Statistically, the differences between the mean
predicted and underlying theoretical spectra are within $3\sigma$. Moreover,
the probability densities obtained from predicted spectra agree very well with
those obtained from actual full sky spectra for each multipole. Equally
interesting is that the correlation matrix calculated from predicted spectra
does not show any signature of correlation between the spectrum of different
multipoles. Our work shows that the predicted spectra do not need to be binned
even at high resolution to rid of correlations due to mode-mode coupling
introduced on the partial sky since the ANN learns to effectively recover the
lost information due to sky cut. The excellent agreement of statistical
properties between the predicted and the ground-truth demonstrates the
importance of using artificial intelligence systems in cosmological analysis
more widely.
