Sparse Inpainting and Isotropy

TL;DR

This paper examines how sparse inpainting methods using spherical harmonics can introduce subtle anisotropies in cosmological maps, particularly affecting higher-order angular polyspectra like the trispectrum.

Contribution

It analytically and empirically investigates the impact of sparse inpainting on the isotropy of CMB maps, highlighting potential biases in higher-order statistics.

Findings

Inpainted maps may show small anisotropies in the trispectrum.

Sparse inpainting can induce non-negligible deviations from isotropy.

Analytic and simulation results support these effects.

Abstract

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.