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This paper introduces a technique called NKL, which cleans both polarized andunpolarized foregrounds from HI intensity maps by applying a Karhunen-Lo\`evetransform on the needlet coefficients. In NKL, one takes advantage ofcorrelations not only along the line of sight, but also between differentangular regions, referred to as ``chunks". This provides a distinct advantageover many of the standard techniques applied to map-space that one finds in theliterature, which do not consider such spatial correlations. Moreover, the NKLtechnique does not require any priors on the nature of the foregrounds, whichis important when considering polarized foregrounds. We also introduce amodified version of GNILC, referred to as MGNILC, which incorporates anapproximation of the foregrounds to improve performance. The NKL and MGNILCtechniques are tested on simulated maps which include polarized foregrounds.Their performance is compared to the GNILC, GMCA, ICA and PCA techniques. Twoseparate 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 $k < 0.1\,{\rmhMpc^{-1}}$ in the higher redshift case and $k < 0.03 \,{\rm hMpc^{-1}}$ in thelower redshift case. However, none of the methods were found to recover thepower spectrum satisfactorily at all BAO scales.

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