Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction

Upcoming Cosmic Microwave Background (CMB) experiments, aimed at measuring primordial CMB B-modes, require exquisite control of Galactic foreground contamination. Minimum-variance techniques, like the Needlet Internal Linear Combination (NILC), have proven effective in reconstructing the CMB polarization signal and mitigating foregrounds across diverse sky models without suffering from mismodelling errors. Still, residual contamination may bias the recovered CMB polarization at large angular scales when confronted with the most complex foreground scenarios. By adding constraints to NILC to deproject moments of the Galactic emission, the Constrained Moment ILC (cMILC) method has proven to enhance foreground subtraction, albeit with an associated increase in overall noise variance. Faced with this trade-off between foreground bias reduction and overall variance minimization, there is still no recipe on which moments to deproject and which are better suited for blind variance minimization. To address this, we introduce the optimized cMILC (ocMILC) pipeline, which performs full optimization of the required number and set of foreground moments to deproject, pivot parameter values, and deprojection coefficients across the sky and angular scales, depending on the actual sky complexity, available frequency coverage, and experiment sensitivity. The optimal number of deprojected moments, before paying significant noise penalty, is determined through a data diagnosis inspired by the Generalized NILC (GNILC) method. Validated on B-mode simulations of the PICO space mission concept with four challenging foreground models, ocMILC exhibits lower foreground contamination compared to NILC and cMILC at all angular scales, with limited noise penalty. This multi-layer optimization enables the ocMILC pipeline to achieve unbiased posteriors of the tensor-to-scalar ratio, regardless of foreground complexity.