Using inpainting to construct accurate cut-sky CMB estimators

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.

21 pages, 10 figures

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• CMB constraints on running non-Gaussianity
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• A Generative Model of Galactic Dust Emission Using Variational Inference
• High-resolution CMB bispectrum estimator with flexible modal basis
• CMB bounds on tensor-scalar-scalar inflationary correlations
• Inpainting CMB maps using Partial Convolutional Neural Networks
• Characterization Of Inpaint Residuals In Interferometric Measurements of the Epoch Of Reionization
• Galaxy cluster SZ detection with unbiased noise estimation: an iterative approach
• Revisiting the large-scale CMB anomalies: The impact of the SZ signal from the Local Universe
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• Constraining graviton non-Gaussianity through the CMB bispectra
• Bayesian recalibration of Planck galaxy cluster scaling relations including relativistic Sunyaev-Zel'dovich corrections
• Inpainting via Generative Adversarial Networks for CMB data analysis
• Constraints on primordial non-Gaussianity from Planck PR4 data
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