Using inpainting to construct accurate cut-sky CMB estimators
H. F. Gruetjen, J. R. Fergusson, M. Liguori, E. P. S. Shellard

TL;DR
This paper investigates inpainting techniques for constructing accurate cut-sky CMB estimators, demonstrating improved performance over traditional methods and exploring their application to power spectrum and bispectrum estimations.
Contribution
The study introduces and compares inpainting-based estimators with existing methods, showing their potential to achieve near-optimal accuracy in cut-sky CMB analysis.
Findings
Inpainting significantly outperforms PCL in power spectrum estimation.
Inpainting can achieve near-optimal bispectrum estimation accuracy.
Appropriate apodisation with low-l cleaning can match inpainting performance.
Abstract
The direct evaluation of manifestly optimal, cut-sky CMB power spectrum and bispectrum estimators is numerically very costly, due to the presence of inverse-covariance filtering operations. This justifies the investigation of alternative approaches. In this work, we mostly focus on an inpainting algorithm that was introduced in recent CMB analyses to cure cut-sky suboptimalities of bispectrum estimators. First, we show that inpainting can equally be applied to the problem of unbiased estimation of power spectra. We then compare the performance of a novel inpainted CMB temperature power spectrum estimator to the popular apodised pseudo- (PCL) method and demonstrate, both numerically and with analytic arguments, that inpainted power spectrum estimates significantly outperform PCL estimates. Finally, we study the case of cut-sky bispectrum estimators, comparing the performance of…
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