Starletℓ₁-norm for weak lensing cosmology

Abstract

We present a new summary statistic for weak lensing observables, higher than second order, suitable for extracting non-Gaussian cosmological information and inferring cosmological parameters. We name this statistic the ‘starlet ℓ1-norm’ as it is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a weak lensing map. In comparison to the state-of-the-art higher-order statistics – weak lensing peak counts and minimum counts, or the combination of the two – the ℓ1-norm provides a fast multi-scale calculation of the full void and peak distribution, avoiding the problem of defining what a peak is and what a void is: the ℓ1-norm carries the information encoded in all pixels of the map, not just the ones in local maxima and minima. We show its potential by applying it to the weak lensing convergence maps provided by the MassiveNus simulations to get constraints on the sum of neutrino masses, the matter density parameter, and the amplitude of the primordial power spectrum. We find that, in an ideal setting without further systematics, the starlet ℓ1-norm remarkably outperforms commonly used summary statistics, such as the power spectrum or the combination of peak and void counts, in terms of constraining power, representing a promising new unified framework to simultaneously account for the information encoded in peak counts and voids. We find that the starlet ℓ1-norm outperforms the power spectrum by 72% on Mν, 60% on Ωm, and 75% on As for the Euclid-like setting considered; it also improves upon the state-of-the-art combination of peaks and voids for a single smoothing scale by 24% on Mν, 50% on Ωm, and 24% on As.

Probabilistic mass-mapping with neural score estimation

“…While most of the cosmological analysis of weak lensing focuses on 2pt functions, the reconstruction of maps of the matter distribution opens up alternative ways to analyze data, including giving access to higher-order statistics, such as the peak count Contact: benjamin.remy@cea.fr statistic, which has been applied to most existing weak lensing surveys (Liu et al 2015a,b;Kacprzak et al 2016;Shan et al 2018;Martinet et al 2018;Harnois-Déraps et al 2020). In addition, novel higher-order statistics such as the wavelet peak counts and 1 -norm (Ajani et al 2021), the scattering transform statistics (Cheng et al 2020), or neural summaries (e.g., Ribli et al 2019;Jeffrey et al 2020a), have recently been shown to be even more sensitive to cosmology.…”

UNIONS: The impact of systematic errors on weak-lensing peak counts

“…Its non-Gaussian part, which is induced by the nonlinear evolution of structure on small scales and low redshifts, contains, however, a wealth of information about cosmology. Several higher-order statistics, such as Minkowski functionals (Kratochvil et al 2012;Parroni et al 2020), higher-order moments (for example, Petri et al 2016;Gatti et al 2020), the bispectrum (Takada & Jain 2004;Coulton et al 2019), peak counts (Kruse & Schneider 1999;Dietrich & Hartlap 2010;Liu et al 2015b;Lin & Kilbinger 2015;Peel et al 2017;Martinet et al 2017;Li et al 2019;Ajani et al 2020, and references therein), the starlet 1 norm (Ajani et al 2021), the scattering transform (Cheng et al 2020), wavelet phase harmonic statistics (Allys et al 2020), and machine learning-based methods (Fluri et al 2018(Fluri et al , 2022Shirasaki et al 2021, among others), have been introduced to account for non-Gaussian information.…”

Starlet higher order statistics for galaxy clustering and weak lensing

“…Specifically for weak lensing, a rich literature proposing several non-Gaussian statistics (Euclid Collaboration 2023), such as Minkowski functionals (e.g., Kratochvil et al 2012 andParroni et al 2020), higher order moments (e.g., Petri et al 2016 andGatti et al 2020), bispectrum (Takada & Jain 2004;Coulton et al 2019), peak counts (Kruse & Schneider 1999;Dietrich & Hartlap 2010;Liu et al 2015;Lin & Kilbinger 2015;Peel et al 2017;Martinet et al 2017;Li et al 2019;Ajani et al 2020;Zücher et al 2022b;Ayçoberry et al 2023), Betti numbers (Parroni et al 2021), the scattering transform (Cheng et al 2020), wavelet phase harmonic statistics (Allys et al 2020), and machine learning-based methods (e.g., Fluri et al 2018 andShirasaki et al 2021), is catching the attention of the community. The 1 -norm of wavelet coefficients of weak-lensing convergence maps has been proposed (Ajani et al 2021) as a new summary statistics for weak lensing as it provides a unified framework to perform a multi-scale analysis that takes into account the information encoded in all pixels of the map.…”