Towards efficient and optimal analysis of CMB anisotropies on a masked sky

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Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-Cₗ framework lead to information loss due to estimator suboptimalities. We set out and validate a methodology for numerically efficient estimators for a masked sky that recover nearly as much information as a full maximum likelihood procedure. In addition to the standard pseudo-Cₗ statistic, the approach introduces an augmented basis designed to account for the mode coupling due to the masking of the sky. We motivate the choice of this basis by describing the basic structure of the covariance matrix. We demonstrate that the augmented estimator can achieve near-optimal results in the presence of a WMAP-realistic mask.