Foreground Mitigation for CMB Lensing with the Global Minimum Variance Quadratic Estimator
Weak gravitational lensing of the cosmic microwave background (CMB) is a powerful probe of cosmology, providing insight into structure formation and the evolution of the universe. Current and upcoming CMB experiments such as SPT-3G and the Simons Observatory (SO) provide high-resolution, low-noise temperature and polarization maps that are ideal for lensing reconstruction. The global minimum variance (GMV) quadratic estimator for CMB lensing reduces reconstruction noise over the standard quadratic estimator (SQE). In this work, we extend the GMV framework to incorporate the tSZ-deproj and cross-ILC foreground mitigation techniques, which enhance robustness against contamination from astrophysical sources. For a simulation study using SPT-3G Ext-10k and SO Extended configurations at $\ell_{\mathrm{max}}^T = 3500$, the lensing bias at $L < 1000$ is reduced from $\sim4\%$ with standard GMV and SQE to $2\%$ with tSZ-deproj, and to $< 1\%$ with cross-ILC. These methods enable the construction of foreground-cleaned lensing maps suitable for cross-correlation analyses, with direct relevance for current and future surveys.