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Separation of the B component of a cosmic microwave background (CMB)polarization map from the much larger E component is an essential step in CMBpolarimetry. For a map with incomplete sky coverage, this separation isnecessarily hampered by the presence of "ambiguous" modes which could be eitherE or B modes. I present an efficient pixel-space algorithm for removing theambiguous modes and separating the map into "pure" E and B components. Themethod, which works for arbitrary geometries, does not involve generating acomplete basis of such modes and scales the cube of the number of pixels on theboundary of the map.

Efficient decomposition of cosmic microwave background polarization maps into pure E, pure B, and ambiguous components