Using inpainting to construct accurate cut-sky CMB estimators

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-$C_l$ (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 three different approaches: inpainting, apodisation and a novel low-l leaning scheme. Providing an analytic argument why the local shape is typically most affected we mainly focus on local type non-Gaussianity. Our results show that inpainting allows to achieve optimality also for bispectrum estimation, but interestingly also demonstrate that appropriate apodisation, in conjunction with low-l cleaning, can lead to comparable accuracy.