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We present new methods for mapping the curl-free (E-mode) and divergence-free(B-mode) components of spin 2 signals using spin directional wavelets. Ourmethods are equally applicable to measurements of the polarisation of thecosmic microwave background (CMB) and the shear of galaxy shapes due to weakgravitational lensing. We derive pseudo and pure wavelet estimators, where E-Bmixing arising due to incomplete sky coverage is suppressed in wavelet spaceusing scale- and orientation-dependent masking and weighting schemes. In thecase of the pure estimator, ambiguous modes (which have vanishing curl anddivergence simultaneously on the incomplete sky) are also cancelled. Onsimulations, we demonstrate the improvement (i.e., reduction in leakage)provided by our wavelet space estimators over standard harmonic spaceapproaches. Our new methods can be directly interfaced in a coherent andcomputationally-efficient manner with component separation or featureextraction techniques that also exploit wavelets.

Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses