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

TL;DR

This paper introduces a harmonic inpainting method to improve the reconstruction of the cosmic microwave background sky within masked regions, significantly reducing errors especially for odd-parity modes in symmetric masks.

Contribution

The paper presents a novel harmonic inpainting algorithm tailored for CMB data, with error estimates and demonstrated improvements over traditional methods.

Findings

Significant error reduction in odd-parity modes for symmetric masks.

Modest improvements in even-parity modes for realistic masks.

Algorithm performs well for scale-invariant Gaussian fluctuations.

Abstract

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.