Comparing Foreground Removal Techniques for Recovery of the LOFAR-EoR
  21cm Power Spectrum
  We compare various foreground removal techniques that are being utilised to
remove bright foregrounds in various experiments aiming to detect the
redshifted 21cm signal of neutral hydrogen from the Epoch of Reionization. In
this work, we test the performance of removal techniques (FastICA, GMCA, and
GPR) on 10 nights of LOFAR data and investigate the possibility of recovering
the latest upper limit on the 21cm signal. Interestingly, we find that GMCA and
FastICA reproduce the most recent 2$\sigma$ upper limit of $\Delta^2_{21} <$
(73)$^2$ mK$^2$ at $k=0.075~ h \mathrm{cMpc}^{-1}$, which resulted from the
application of GPR. We also find that FastICA and GMCA begin to deviate from
the noise-limit at \textit{k}-scales larger than $\sim 0.1 ~h
\mathrm{cMpc}^{-1}$. We then replicate the data via simulations to see the
source of FastICA and GMCA's limitations, by testing them against various
instrumental effects. We find that no single instrumental effect, such as
primary beam effects or mode-mixing, can explain the poorer recovery by FastICA
and GMCA at larger \textit{k}-scales. We then test scale-independence of
FastICA and GMCA, and find that lower \textit{k}-scales can be modelled by a
smaller number of independent components. For larger scales ($k \gtrsim 0.1~h
\mathrm{cMpc}^{-1}$), more independent components are needed to fit the
foregrounds. We conclude that, the current usage of GPR by the LOFAR
collaboration is the appropriate removal technique. It is both robust and less
prone to overfitting, with future improvements to GPR's fitting optimisation to
yield deeper limits.
