Exploring the Cosmic Reionization Epoch in Frequency Space: An Improved
  Approach to Remove the Foreground in 21 cm Tomography
  Aiming to correctly restore the redshifted 21 cm signals emitted by the
neutral hydrogen during the cosmic reionization processes, we re-examine the
separation approaches based on the quadratic polynomial fitting technique in
frequency space to investigate whether they works satisfactorily with complex
foreground, by quantitatively evaluate the quality of restored 21 cm signals in
terms of sample statistics. We construct the foreground model to characterize
both spatial and spectral substructures of the real sky, and use it to simulate
the observed radio spectra. By comparing between different separation
approaches through statistical analysis of restored 21 cm spectra and
corresponding power spectra, as well as their constraints on the mean halo bias
$b$ and average ionization fraction $x_e$ of the reionization processes, at
$z=8$ and the noise level of 60 mK we find that, although the complex
foreground can be well approximated with quadratic polynomial expansion, a
significant part of Mpc-scale components of the 21 cm signals (75% for $\gtrsim
6h^{-1}$ Mpc scales and 34% for $\gtrsim 1h^{-1}$ Mpc scales) is lost because
it tends to be mis-identified as part of the foreground when
single-narrow-segment separation approach is applied. The best restoration of
the 21 cm signals and the tightest determination of $b$ and $x_e$ can be
obtained with the three-narrow-segment fitting technique as proposed in this
paper. Similar results can be obtained at other redshifts.
