Needlet Karhunen-Lo\`eve (NKL): A Method For Cleaning Foregrounds From 21cm Intensity Maps

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.