  This paper introduces a technique called NKL, which cleans both polarized and
unpolarized foregrounds from HI intensity maps by applying a Karhunen-Lo\`eve
transform on the needlet coefficients. In NKL, one takes advantage of
correlations not only along the line of sight, but also between different
angular regions, referred to as ``chunks". This provides a distinct advantage
over many of the standard techniques applied to map-space that one finds in the
literature, which do not consider such spatial correlations. Moreover, the NKL
technique does not require any priors on the nature of the foregrounds, which
is important when considering polarized foregrounds. We also introduce a
modified version of GNILC, referred to as MGNILC, which incorporates an
approximation of the foregrounds to improve performance. The NKL and MGNILC
techniques are tested on simulated maps which include polarized foregrounds.
Their performance is compared to the GNILC, GMCA, ICA and PCA techniques. Two
separate tests were performed. One at $1.84 < z < 2.55$ and the other at $0.31
< z < 0.45$. NKL was found to provide the best performance in both tests,
providing a factor of 10 to 50 improvement over GNILC at $k < 0.1\,{\rm
hMpc^{-1}}$ in the higher redshift case and $k < 0.03 \,{\rm hMpc^{-1}}$ in the
lower redshift case. However, none of the methods were found to recover the
power spectrum satisfactorily at all BAO scales.
