  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-C_l
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-C_l 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.
