Methods for pixel domain correction of EB leakage

Understand

In observation of the cosmic microwave background (CMB) polarization, "$EB$~leakage" refers to the artificial $B$-mode signal coming from the leakage of $E$-mode signal when part of the sky is unavailable or excluded.

• Correction of such leakage is one of the preconditions for detecting primordial gravitational waves via the CMB $B$-mode signal.
• In this work, we design two independent methods for correcting the $EB$~leakage directly in the pixel domain using standard definitions of the $E$- and $B$-modes.
• The two methods give consistent results, and both are fast and easy to implement.