Recovery of 21 cm intensity maps with sparse component separation
  21 cm intensity mapping has emerged as a promising technique to map the
large-scale structure of the Universe. However, the presence of foregrounds
with amplitudes orders of magnitude larger than the cosmological signal
constitutes a critical challenge. Here, we test the sparsity-based algorithm
Generalised Morphological Component Analysis (GMCA) as a blind component
separation technique for this class of experiments. We test the GMCA
performance against realistic full-sky mock temperature maps that include,
besides astrophysical foregrounds, also a fraction of the polarized part of the
signal leaked into the unpolarized one, a very troublesome foreground to
subtract, usually referred to as polarization leakage. To our knowledge, this
is the first time the removal of such component is performed with no prior
assumption. We assess the success of the cleaning by comparing the true and
recovered power spectra, in the angular and radial directions. In the best
scenario looked at, GMCA is able to recover the input angular (radial) power
spectrum with an average bias of $\sim 5\%$ for $\ell>25$ ($20 - 30 \%$ for
$k_{\parallel} \gtrsim 0.02 \,h^{-1}$Mpc), in the presence of polarization
leakage. Our results are robust also when up to $40\%$ of channels are missing,
mimicking a Radio Frequency Interference (RFI) flagging of the data. Having
quantified the notable effect of polarisation leakage on our results, in
perspective we advocate the use of more realistic simulations when testing 21
cm intensity mapping capabilities.
