Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise

We present an augmented version of our dual messenger algorithm for spin field reconstruction on the sphere, while accounting for highly non-trivial and realistic noise models such as modulated correlated noise. We also describe an optimization method for the estimation of noise covariance from Monte Carlo simulations. Using simulated Planck polarized cosmic microwave background (CMB) maps as a showcase, we demonstrate the capabilities of the algorithm in reconstructing pure E and B maps, guaranteed to be free from ambiguous modes resulting from the leakage or coupling issue that plagues conventional methods of E/B separation. Due to its high speed execution, coupled with lenient memory requirements, the algorithm can be optimized in exact global Bayesian analyses of state-of-the-art CMB data for a statistically optimal separation of pure E and B modes. Our algorithm, therefore, has a potentially key role in the data analysis of high-resolution and high-sensitivity CMB data, especially with the range of upcoming CMB experiments tailored for the detection of the elusive primordial B-mode signal.