A Bayesian analysis of redshifted 21-cm HI signal and foregrounds:
  Simulations for LOFAR
  Observations of the EoR with the 21-cm hyperfine emission of neutral hydrogen
(HI) promise to open an entirely new window onto the formation of the first
stars, galaxies and accreting black holes. In order to characterize the weak
21-cm signal, we need to develop imaging techniques which can reconstruct the
extended emission very precisely. Here, we present an inversion technique for
LOFAR baselines at NCP, based on a Bayesian formalism with optimal spatial
regularization, which is used to reconstruct the diffuse foreground map
directly from the simulated visibility data. We notice the spatial
regularization de-noises the images to a large extent, allowing one to recover
the 21-cm power-spectrum over a considerable $k_{\perp}-k_{\para}$ space in the
range of $0.03\,{\rm Mpc^{-1}}<k_{\perp}<0.19\,{\rm Mpc^{-1}}$ and $0.14\,{\rm
Mpc^{-1}}<k_{\para}<0.35\,{\rm Mpc^{-1}}$ without subtracting the noise
power-spectrum. We find that, in combination with using the GMCA, a
non-parametric foreground removal technique, we can mostly recover the
spherically average power-spectrum within $2\sigma$ statistical fluctuations
for an input Gaussian random rms noise level of $60 \, {\rm mK}$ in the maps
after 600 hrs of integration over a $10 \, {\rm MHz}$ bandwidth.
