General solution to the E-B mixing problem

We derive a general ansatz for optimizing pseudo-C-center dot estimators used to measure cosmic microwave background anisotropy power spectra, and apply it to the recently proposed pure pseudo-C-center dot formalism, to obtain an estimator which achieves near-optimal B-mode power spectrum errors for any specified noise distribution while minimizing leakage from ambiguous modes. Our technique should be relevant for upcoming cosmic microwave background polarization experiments searching for B-mode polarization. We compare our technique both to the theoretical limits based on a full Fisher matrix calculation and to the standard pseudo-C-center dot technique. We demonstrate it by applying it to a fiducial survey with realistic inhomogeneous noise, complex boundaries, point source masking, and a noise level comparable to what is expected for next-generation experiments (similar to 5.75 mu K-arcmin). For such an experiment our technique could improve the constraints on the amplitude of a gravity wave background by over a factor of 10 compared to what could be obtained using ordinary pseudo-C-center dot, coming quite close to saturating the theoretical limit. Constraints on the amplitude of the lensing B-modes are improved by about a factor of 3.