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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.
This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. Th
We develop an algorithm of separating the $E$ and $B$ modes of the CMB polarization from the noisy and discretized maps of Stokes parameter $Q$ and $U$ in a finite area. A key step of the algorithm is to take a wavelet-Galerkin discretization of the
Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarizati
A crucial problem for partial sky analysis of CMB polarization is the $E$-$B$ leakage problem. Such leakage arises from the presence of `ambiguous modes that satisfy properties of both $E$ and $B$ modes. Solving this problem is critical for primordia
In the late seventies, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721-734, Sijthoff & Noordhoff] pointed out that it would be natural for $pi_t$, the solution of the stocha