Non-Gaussian modelling and statistical denoising of Planck dust polarisation full-sky maps using scattering transforms

Abstract

Scattering transforms have been successfully used to describe dust polarisation for flat-sky images. This paper expands this framework to noisy observations on the sphere with the aim of obtaining denoised Stokes Q and U all-sky maps at 353 GHz, as well as a non-Gaussian model of dust polarisation, from the Planck data. To achieve this goal, we extended the computation of scattering coefficients to the HEALPix pixelation and introduced cross-statistics that allowed us to make use of half-mission maps as well as the correlation between dust temperature and polarisation. Introducing a general framework, we developed an algorithm that uses the scattering statistics to separate dust polarisation from data noise. The separation was validated on mock data before it was applied to the SRoll2 Planck maps at N side = 256. The validation shows that the statistics of the dust emission, including its non-Gaussian properties, are recovered until max ∼ 700, where, at high Galactic latitudes, the dust power is weaker than that of the dust by two orders of magnitude. On scales where the dust power is weaker than one-tenth of the power of the noise, structures in the output maps have comparable statistics, but are not spatially coincident with those of the input maps. Our results on Planck data are significant milestones opening new perspectives for statistical studies of dust polarisation and for the simulation of Galactic polarised foregrounds. The Planck denoised maps are available (see ftp://sroll20.ias.u-psud.fr/sroll40_353) together with results from our validation on mock data, which may be used to quantify uncertainties.

Probing the Cold Neutral Medium through H I Emission Morphology with the Scattering Transform

“…The ST was originally proposed by Mallat (2012) in the context of signal processing in computer vision, to extract information from high-dimensional input fields. There has been growing interest in applying the ST to astrophysical data analysis (e.g., Robitaille et al 2014;Allys et al 2019;Cheng et al 2020;Regaldo-Saint Blancard et al 2020;Chung 2022;Delouis et al 2022;Valogiannis & Dvorkin 2022;Greig et al 2023). This derives from the ST's capacity to encode substantial non-Gaussian information, in a set of coefficients that are intuitively meaningful.…”

“…We characterize the H I morphology by using the scattering transform (ST), which is a powerful statistical technique capable of extracting significant non-Gaussian information into a set of compact and interpretable coefficients. Recent applications of the ST include ISM studies of non-Gaussian structures in dust emission (e.g., Robitaille et al 2014;Allys et al 2019;Regaldo-Saint Blancard et al 2020;Saydjari et al 2021;Delouis et al 2022) as well as cosmological parameter inference in contexts such as large-scale structure (Cheng et al 2020;Valogiannis & Dvorkin 2022) and line intensity mapping (Chung 2022;Greig et al 2023). Compared to dedicated filament finders like the RHT, the ST is a far more flexible and general descriptor of field morphology.…”

Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

“…Taking into account the multichannel aspect of the data should provide more accurate estimations of the statistics of the noise-free emission since observations at different frequency bands are usually affected by independent noise processes. Note that very recently, and in parallel to this work, a significant step has been taken in this direction by Delouis et al (2022) employing WST statistics. In that paper, the authors extended the WST to the sphere and introduced cross-WST statistics to characterize correlations across observables in order to statistically denoise Planck all-sky maps of the dust emission.…”

Filamentary Dust Polarization and the Morphology of Neutral Hydrogen Structures

“…Future work could consider additional metrics, including those sensitive to non-Gaussian structures in the dust, e.g., Minkowski functionals (Mantz et al 2008) or the scattering transform (Mallat 2011). These techniques have recently been used to quantify structures in dust (Delouis et al 2022) and in H I emission (Lei & Clark 2023) individually.…”