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A new spin wavelet transform on the sphere is proposed to analyse thepolarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signalobserved on the celestial sphere. The scalar directional scale-discretisedwavelet transform on the sphere is extended to analyse signals of arbitraryspin. The resulting spin scale-discretised wavelet transform probes thedirectional intensity of spin signals. A procedure is presented using this newspin wavelet transform to recover E- and B-mode signals from partial-skyobservations of CMB polarisation.

On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation