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 ne
ed 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 $2sigma$ 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.
The exceptional sensitivity of the SKA will allow observations of the Cosmic Dawn and Epoch of Reionization (CD/EoR) in unprecedented detail, both spectrally and spatially. This wealth of information is buried under Galactic and extragalactic foregro
unds, which must be removed accurately and precisely in order to reveal the cosmological signal. This problem has been addressed already for the previous generation of radio telescopes, but the application to SKA is different in many aspects. In this chapter we summarise the contributions to the field of foreground removal in the context of high redshift and high sensitivity 21-cm measurements. We use a state-of-the-art simulation of the SKA Phase 1 observations complete with cosmological signal, foregrounds and frequency-dependent instrumental effects to test both parametric and non-parametric foreground removal methods. We compare the recovered cosmological signal using several different statistics and explore one of the most exciting possibilities with the SKA --- imaging of the ionized bubbles. We find that with current methods it is possible to remove the foregrounds with great accuracy and to get impressive power spectra and images of the cosmological signal. The frequency-dependent PSF of the instrument complicates this recovery, so we resort to splitting the observation bandwidth into smaller segments, each of a common resolution. If the foregrounds are allowed a random variation from the smooth power law along the line of sight, methods exploiting the smoothness of foregrounds or a parametrization of their behaviour are challenged much more than non-parametric ones. However, we show that correction techniques can be implemented to restore the performances of parametric approaches, as long as the first-order approximation of a power law stands.
Several experiments are underway to detect the cosmic redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by
measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signals power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation and parameter estimation pipeline developed for the Low Frequency Array (LOFAR)-EoR experiment. We show that LOFAR should be able to detect the EoR in 600 hours of integration using the variance statistic. Additionally, the redshift ($z_r$) and duration ($Delta z$) of reionization can be constrained assuming a parametrization. We use an EoR simulation of $z_r = 7.68$ and $Delta z = 0.43$ to test the pipeline. We are able to detect the simulated signal with a significance of 4 standard deviations and extract the EoR parameters as $z_r = 7.72^{+0.37}_{-0.18}$ and $Delta z = 0.53^{+0.12}_{-0.23}$ in 600 hours, assuming that systematic errors can be adequately controlled. We further show that the significance of detection and constraints on EoR parameters can be improved by measuring the cross-variance of the signal by cross-correlating consecutive redshift bins.
