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Extragalactic foregrounds in temperature maps of the Cosmic MicrowaveBackground (CMB) severely limit the ability of standard estimators toreconstruct the weak lensing potential. These foregrounds are not fullyremovable by multi-frequency cleaning or masking and can lead to large biasesif not properly accounted for. For foregrounds made of a number of unclusteredpoint sources, an estimator for the source amplitude can be derived anddeprojected, removing any bias to the lensing reconstruction. We show withsimulations that all of the extragalactic foregrounds in temperature can beapproximated by a collection of sources with identical profiles, and that asimple bias hardening technique is effective at reducing any bias to lensing,at a minimal noise cost. We compare the performance and bias to other methodssuch as "shear-only" reconstruction, and discuss how to jointly deproject anyarbitrary number of foregrounds, each with an arbitrary profile. In particular,for a Simons Observatory-like experiment foreground-hardened estimators allowus to extend the maximum multipole used in the reconstruction, increasing theoverall statistical power by $\sim 50\%$ over the standard quadratic estimator,both in auto and cross-correlation. We conclude that source hardeningoutperforms the standard lensing quadratic estimator both in auto andcross-correlation, and in terms of lensing signal-to-noise and foreground bias.

Lower bias, lower noise CMB lensing with foreground-hardened estimators