The RWST, a comprehensive statistical description of the non-Gaussian structures in the ISM

Allys, Erwan; Levrier, F.; Zhang, S.; Colling, Cédric; Blancard, Bruno Régaldo-Saint; Boulanger, F.; Hennebelle, P.; Mallat, Stéphane

doi:10.1051/0004-6361/201834975

Cited by 54 publications

(79 citation statements)

References 70 publications

(89 reference statements)

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“…In addition,Ŝ iso,1 2 coefficients for R[Q + iŨ] show a scale invariance property:Ŝ iso,1 2 coefficients only depend on the difference j 2 − j 1 . We point out that these scale invariant patterns are signatures of scale invariant Gaussian processes (Bruna et al 2015) and have already been observed for fractional Brownian motions processes in Allys et al (2019).…”

Section: Second Order Coefficients and Non-gaussianity Of The Datasupporting

confidence: 69%

“…XLII 2016; Ghosh et al 2017;Vansyngel et al 2017;Levrier et al 2018;Adak et al 2020;Clark & Hensley 2019) or directly from numerical simulations (Kim et al 2019). It follows what has been done for dust total intensity by Allys et al (2019) using the RWST, and Aylor et al (2019) using a Generative Adversarial Network.…”

Section: Random Syntheses Ofq + Iũ Polarization Mapsmentioning

confidence: 78%

“…This is because the WST relies on nonexpansive operators (see Bruna & Mallat 2013). Originally designed to understand the properties of deep convolutional neural networks which have proved successful for classification problems (LeCun et al 2010;Krizhevsky et al 2012), this tool also provides a convenient statistical description of astronomical observations of the interstellar medium for total intensity A&A 642, A217 (2020) maps (Allys et al 2019). In this subsection we use the WST to describe the statistical properties of the polarization related maps discussed in the previous section: complex mapsQ + iŨ and exp(2iψ), and real map p. Let us briefly recall the definition of the WST of a given 2D real field I(x) that is statistically homogeneous 5 .…”

Section: Wst Statistical Descriptionmentioning

confidence: 99%

“…In this subsection we use the WST to describe the statistical properties of the polarization related maps discussed in the previous section: complex mapsQ + iŨ and exp(2iψ), and real map p. Let us briefly recall the definition of the WST of a given 2D real field I(x) that is statistically homogeneous 5 . For a more complete presentation we refer to Allys et al (2019) and Bruna & Mallat (2013). The WST relies on convolutions of the target field I(x) with a set of J × Θ Morlet wavelets ψ j,θ with 0 ≤ j ≤ J − 1 and θ ∈ {kπ/Θ, 0 ≤ k ≤ Θ − 1}, with J and Θ two integers.…”

Section: Wst Statistical Descriptionmentioning

confidence: 99%

“…If synthetic total intensity maps generated from a RWST description have already been produced in Allys et al (2019), in this paper we extend and improve this procedure for complex polarization mapsQ + iŨ. We give in this subsection some technical details on the implementation but details on the mathematical formalism can be found in Bruna & Mallat (2019).…”

Section: Generation Of Synthetic Polarization Maps From a Rwst Descrimentioning

confidence: 99%

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Statistical description of dust polarized emission from the diffuse interstellar medium

Blancard

Levrier

Allys

et al. 2020

A&A

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The statistical characterization of the diffuse magnetized interstellar medium (ISM) and Galactic foregrounds to the cosmic microwave background (CMB) poses a major challenge. To account for their non-Gaussian statistics, we need a data analysis approach capable of efficiently quantifying statistical couplings across scales. This information is encoded in the data, but most of it is lost when using conventional tools, such as one-point statistics and power spectra. The wavelet scattering transform (WST), a low-variance statistical descriptor of non-Gaussian processes introduced in data science, opens a path towards this goal. To establish the methodology, we applied the WST to noise-free maps of dust polarized thermal emission computed from a numerical simulation of magnetohydrodynamical turbulence in the diffuse ISM. We analyzed normalized complex Stokes maps and maps of the polarization fraction and polarization angle. The WST yields a few thousand coefficients; some of them measure the amplitude of the signal at a given scale, and the others characterize the couplings between scales and orientations. The dependence on orientation can be fitted with the reduced wavelet scattering transform (RWST), an angular model introduced in previous works for total intensity maps. The RWST provides a statistical description of the polarization maps, quantifying their multiscale properties in terms of isotropic and anisotropic contributions. It allowed us to exhibit the dependence of the map structure on the orientation of the mean magnetic field and to quantify the non-Gaussianity of the data. We also used RWST coefficients, complemented by additional constraints, to generate random synthetic maps with similar statistics. Their agreement with the original maps demonstrates the comprehensiveness of the statistical description provided by the RWST. This work is a step forward in the analysis of observational data and the modeling of CMB foregrounds. We also release PyWST, a public Python package to perform WST and RWST analyses of two-dimensional data.

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Section: Second Order Coefficients and Non-gaussianity Of The Datasupporting

confidence: 69%

Section: Random Syntheses Ofq + Iũ Polarization Mapsmentioning

confidence: 78%

Section: Wst Statistical Descriptionmentioning

confidence: 99%

Section: Wst Statistical Descriptionmentioning

confidence: 99%

Section: Generation Of Synthetic Polarization Maps From a Rwst Descrimentioning

confidence: 99%

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Statistical description of dust polarized emission from the diffuse interstellar medium

Blancard

Levrier

Allys

et al. 2020

A&A

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On generalizations of the nonwindowed scattering transform

Chua,

Hirn,

Little

2024

Applied and Computational Harmonic Analysis

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Probing the cold magnetised Universe with SPICA-POL (B-BOP)

André

Hughes

Guillet

et al. 2019

Publ. Astron. Soc. Aust.

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SPICA, the cryogenic infrared space telescope recently pre-selected for a "Phase A" concept study as one of the three remaining candidates for ESA's fifth medium class (M5) mission, is foreseen to include a far-infrared polarimetric imager (SPICA-POL, now called B-BOP), which would offer a unique opportunity to resolve major issues in our understanding of the nearby, cold magnetized Universe. This paper presents an overview of the main science drivers for B-BOP, including high dynamic range polarimetric imaging of the cold interstellar medium (ISM) in both our Milky Way and nearby galaxies. Thanks to a cooled telescope, B-BOP will deliver wide-field 100-350 µm images of linearly polarized dust emission in Stokes Q and U with a resolution, signal-to-noise ratio, and both intensity and spatial dynamic ranges comparable to those achieved by Herschel images of the cold ISM in total intensity (Stokes I). The B-BOP 200 µm images will also have a factor ∼ 30 higher resolution than Planck polarization data. This will make B-BOP a unique tool for characterizing the statistical properties of the magnetized interstellar medium and probing the role of magnetic fields in the formation and evolution of the interstellar web of dusty molecular filaments giving birth to most stars in our Galaxy. B-BOP will also be a powerful instrument for studying the magnetism of nearby galaxies and testing galactic dynamo models, constraining the physics of dust grain alignment, informing the problem of the interaction of cosmic rays with molecular clouds, tracing magnetic fields in the inner layers of protoplanetary disks, and monitoring accretion bursts in embedded protostars.

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The RWST, a comprehensive statistical description of the non-Gaussian structures in the ISM

Cited by 54 publications

References 70 publications

Statistical description of dust polarized emission from the diffuse interstellar medium

Statistical description of dust polarized emission from the diffuse interstellar medium

On generalizations of the nonwindowed scattering transform

Probing the cold magnetised Universe with SPICA-POL (B-BOP)

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