Harmonic Inpainting of the Cosmic Microwave Background Sky: Formulation and Error Estimate

We develop a new interpolation scheme, based on harmonic inpainting, for reconstructing the cosmic microwave background temperature data within the Galaxy mask from the data outside the mask. We find that, for scale-invariant isotropic random Gaussian fluctuations, the developed algorithm reduces the errors in the reconstructed map for the odd-parity modes significantly for azimuthally symmetric masks with constant galactic latitudes. For a more realistic Galaxy mask, we find a modest improvement in the even-parity modes as well.