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 $k_{\perp }-k_{\text{para}}$ space in the range of $0.03\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}<k_{\perp }<0.19\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ 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 $60\mathrm{m}\mathrm{K}$ in the maps after 600 hrs of integration over a $10\mathrm{M}\mathrm{H}\mathrm{z}$ bandwidth.