arxiv: 2605.08895 · v1 · submitted 2026-05-09 · 🌌 astro-ph.CO

Recognition: no theorem link

Beyond power spectrum to unveil systematics on HI intensity maps

Pauline Gorbatchev , Jean-Luc Starck , Stefano Camera , Marta Spinelli

Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:18 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords HI intensity mappingstarlet l1-normnon-Gaussian statisticscosmological parametersangular power spectrumsystematic effectsneural density estimationintensity mapping surveys

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The pith

The starlet l1-norm applied to HI intensity maps improves constraints on cosmological parameters by nearly three times over the angular power spectrum.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether a multi-scale higher-order statistic can recover cosmological information from HI intensity maps that the standard angular power spectrum misses. The authors generate thousands of full-sky simulated maps at redshift 0.4 to 0.45 using a lognormal model that includes noise and beam effects, then extract both the starlet l1-norm and the power spectrum from each realization. They feed these summary statistics into a neural density estimator to infer cosmological parameters and compare the resulting precision. A sympathetic reader would care because HI intensity mapping can survey huge volumes efficiently, yet two-point statistics leave non-Gaussian signals from nonlinear structure growth untapped. If the claimed improvement holds, the same observations could yield substantially tighter limits on the matter density and other parameters.

Core claim

We extend the starlet l1-norm, a multi-scale higher-order statistic previously applied to weak lensing maps, to the brightness temperature fluctuations of the HI density field. The HI signal is highly non-Gaussian at late times due to nonlinear structure growth. The starlet l1-norm significantly outperforms the angular power spectrum in constraining cosmological parameters, achieving almost a 3x improvement in the figure of merit relative to the angular power spectrum by capturing non-Gaussian features missed by two-point statistics. Moreover, our results suggest that the starlet l1-norm is robust to several of the systematic effects included in our simulations. Our findings highlight the潜在l

What carries the argument

The starlet l1-norm, which measures the l1-norm of wavelet coefficients across multiple scales to summarize non-Gaussian fluctuations in the brightness temperature maps.

If this is right

Cosmological parameters such as the matter density can be constrained more tightly using the same HI maps.
The statistic continues to deliver improved constraints when realistic noise and telescope beam effects are present.
Non-Gaussian information in the HI field at z approximately 0.4 becomes accessible for parameter estimation.
The approach can be applied directly to data from ongoing or future intensity mapping surveys like MeerKLASS.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method may help isolate cosmological signals from certain instrumental systematics that affect power spectra more strongly.
Similar multi-scale statistics could be tested on other tracers of large-scale structure where non-Gaussianity is also important.
Combining the starlet l1-norm with power spectrum measurements on the same maps might yield even stronger constraints than either alone.

Load-bearing premise

The lognormal model used to generate the simulated HI brightness temperature maps faithfully reproduces the true non-Gaussian statistics of real data, and the neural density estimation recovers unbiased posteriors without hidden biases from the simulation choices or training procedure.

What would settle it

A direct measurement showing that the starlet l1-norm distributions from actual MeerKLASS HI observations deviate substantially from those in the lognormal simulations, or that parameter constraints from real data are no tighter than those from the power spectrum.

Figures

Figures reproduced from arXiv: 2605.08895 by Jean-Luc Starck, Marta Spinelli, Pauline Gorbatchev, Stefano Camera.

**Figure 2.** Figure 2: Sky map with masks. The contours show the mask edges: [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Zoomed maps of different systematic effects + beam (0.5 deg). Panel a: Hi beamed map with no systematic effect. Panel b: Hi beamed map with multiplicative stripe stripe patterns. Panel c: Hi map with residual Galactic synchrotron contamination beamed. Panel d: Hi map with residual extragalactic point source contamination beamed. Panel e: Hi beamed map with multiplicative Xshaped scanning patterns [PITH_F… view at source ↗

**Figure 4.** Figure 4: Relative difference of maps from [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Variability of angular power spectrum over 100 randomly [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 7.** Figure 7: ℓ1-norms of the starlet coefficients as a function of the bin thresholds for different wavelet scales. Each curve corresponds to a wavelet scale, showing how the distribution of coefficients changes across scales. The bins correspond to S/N thresholds or coefficient magnitudes, depending on the normalization [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: Variability of starlet ℓ1-norm over 100 randomly selected realizations with different cosmologies (gray) varying as in [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗

**Figure 9.** Figure 9: Posterior distributions for Ωc , h, and As obtained from the angular power spectrum, Cℓ (left), and starlet ℓ1- norm (right) for different sky fractions, fsky (blue: 0.014, green: 0.19, magenta: 0.6, orange: 1.0). Contours correspond to 68% and 95% confidence levels [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: Posterior comparison between the angular power spectrum (left) and the starlet ℓ1-norm (right) estimators for different beam sizes, all with masked maps of fsky = 0.19. The solid lines show the 1D marginalized posterior distributions, while the shaded regions correspond to the 68% and 95% confidence contours for the parameter pairs (Ωc , h, 10−9 ×As). Blue for a Gaussian beam of FWHM = 1.34◦ . Green show… view at source ↗

**Figure 11.** Figure 11: Cℓ (left), starlet ℓ1-norm (right) for clean map (blue), beamed map 0.5 ◦ (magenta), and beamed + map with instrumental noise (cyan) all maps masked at fsky=0.19. 0.2 0.3 0.4 0.5 Ωc 0.1 0.2 0.3 10 −9 × As 0.5 0.6 0.7 0.8 0.9 h 0.5 0.6 0.7 0.8 0.9 h 0.1 0.2 0.3 10−9 × As Posterior Comparison: Starlet `1-norm vs C` fsky = 0.19, beam = 0.5 ◦ C` Starlet `1-norm 5 scales Starlet `1-norm 8 scales 0.2 0.3 0.4 0… view at source ↗

**Figure 12.** Figure 12: Posterior distributions for Ωc , h, and As comparing the standard power spectrum, Cℓ (blue), to the starlet ℓ1- norm statistic with five scales (magenta) and with eight scales (green), all computed from beamed 0.5 ◦ maps with fsky = 0.19 and noiseless case (left), or the case with instrumental noise (right). 5.4. Beamed, masked maps affected by systematic stripe patterns We assessed the impact of complex… view at source ↗

**Figure 13.** Figure 13: Posterior distributions for Ωc, h, As , and another parameter obtained from the angular power spectrum, Cℓ , starlet ℓ1-norm for beamed maps 0.5 ◦ with sky fraction fsky = 0.19: multiplicative stripes (A = 1.5, w = 2.4 ◦ ; first panel), multiplicative stripes (A = 1.5, w = 2.4 ◦ ) + instrumental noise (second panel), additive stripes (third panel), and additive stripes + noise (fourth panel). Contours cor… view at source ↗

**Figure 14.** Figure 14: Cℓ (first panel), starlet ℓ1-norm with five scales (second panel) and starlet ℓ1-norm with eight scales (third panel), map without systematic effects (orange), map with multiplicative stripes (magenta), map with additive stripes (green), map with extragalactic point sources residuals (blue), map with Galactic synchrotron residuals (sky blue) and map with X-shape pattern (black). All maps are fsky=0.19 an… view at source ↗

**Figure 15.** Figure 15: Posterior distributions for Ωc, h, and As obtained from the angular power spectrum, Cℓ , starlet ℓ1-norm (without coarse scale) for different Galactic synchrotron residual fractions: 0.0005 % (first panel), 0.001 % (second panel), and 0.002 % (third panel). The contours correspond to 68% and 95% confidence levels [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗

**Figure 16.** Figure 16: Posterior distributions for Ωc, h, and As obtained from the angular power spectrum, Cℓ , starlet ℓ1-norm (without coarse scale) for different extragalactic point sources residual fractions: 0.001 % (first panel), 0.0025 % (second panel), and 0.005 % (third panel). The contours correspond to 68% and 95% confidence levels. yields similar results to the residual contamination from Galactic synchrotron and ex… view at source ↗

**Figure 17.** Figure 17: Posterior distributions for Ωc, h, As , and another parameter obtained from the angular power spectrum, Cℓ , starlet ℓ1-norm for different multiplicative X shape weights: 10X (first panel), 25X (second panel), 35X (third panel), and 50X (fourth panel). The contours correspond to 68% and 95% confidence levels. modes, would be influenced very little by the lowest-ℓ modes even if they were included, and is t… view at source ↗

read the original abstract

HI intensity mapping is a promising technique to probe large-scale structure, traditionally analyzed via two-point statistics such as the angular power spectrum. This technique has proven very powerful but may miss key non-Gaussian information present in the signal. We extend the starlet l1-norm, a multi-scale higher-order statistic previously applied to weak lensing maps, to the brightness temperature fluctuations of the HI density field. The HI signal is highly non-Gaussian at late times (z < 1) due to nonlinear structure growth, motivating the use of advanced summary statistics. We simulated full-sky HI lognormal brightness temperature maps using CAMB and GLASS, generating 10,000 realizations with associated cosmological parameters. We extracted both the starlet l1-norm and angular power spectrum from these maps. Using the JaxILI framework, we performed neural density estimation for implicit likelihood inference. The analysis considered simulated maps incorporating realistic noise and telescope beam, capturing the impact of observational effects on parameter inference. In this work, we focus on the redshift range 0.4 < z < 0.45, chosen to match the interval already targeted by existing MeerKLASS observations. The starlet l1-norm significantly outperforms the angular power spectrum in constraining cosmological parameters, achieving almost a 3x improvement in the figure of merit relative to the angular power spectrum by capturing non-Gaussian features missed by two-point statistics. Moreover, our results suggest that the starlet l1-norm is robust to several of the systematic effects included in our simulations. Our findings highlight the potential of multi-scale higher-order statistics such as the starlet l1-norm to enhance cosmological inference from future HI intensity mapping surveys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows the starlet l1-norm beats the power spectrum by nearly 3x in figure of merit on lognormal HI maps, but that gain rests on simulations whose non-Gaussianity may not match real fields.

read the letter

The main point is straightforward: on 10,000 full-sky lognormal HI brightness-temperature maps at z~0.4 with added noise and beam, the starlet l1-norm delivers almost three times the figure of merit of the angular power spectrum when both are fed into the same neural density estimator. The work extends a statistic already used on weak-lensing maps and runs a clean head-to-head test that includes observational effects matching MeerKLASS targets. That quantitative comparison under controlled conditions is the useful piece here. It gives analysts a concrete number to consider when deciding whether to add multi-scale higher-order summaries to their pipelines. The robustness tests against noise and beam are also a practical plus, showing the statistic does not collapse immediately when those systematics are present. The central limitation is the simulation choice. Lognormal fields impose a fixed functional form on the one-point PDF and higher correlations that differs from the skewness and filamentary structure generated by gravitational instability in N-body or hydro runs. Because the l1-norm is built to capture exactly those multi-scale non-Gaussian features, any mismatch between the mock and reality directly affects whether the reported gain survives on actual data. The abstract supplies no cross-check against more realistic mocks, so the factor-of-three claim remains internally consistent but externally provisional. Details on neural estimator validation, such as posterior coverage or parameter recovery on held-out sets, are also thin. This paper is for people already working on HI intensity mapping analysis who need a ready-to-test higher-order statistic. It is not a new framework, but the direct comparison and systematic tests make it worth a look for that audience. It deserves peer review. The execution is focused enough that referees can usefully press on the simulation fidelity and inference checks rather than reject the idea outright.

Referee Report

2 major / 2 minor

Summary. The paper claims that the starlet l1-norm, a multi-scale higher-order statistic, significantly outperforms the angular power spectrum for cosmological parameter inference from HI intensity maps. Using 10,000 full-sky lognormal brightness-temperature realizations generated with CAMB+GLASS at 0.4<z<0.45 (including noise and beam), neural density estimation via JaxILI yields an almost 3x improvement in figure of merit by capturing non-Gaussian information missed by two-point statistics; the analysis targets the MeerKLASS redshift range and reports robustness to included systematics.

Significance. If the central result holds, the work would demonstrate the potential of multi-scale higher-order statistics to improve constraints from future HI intensity mapping surveys beyond standard power-spectrum analyses. The use of 10,000 realizations and an implicit-likelihood neural framework is a clear strength, enabling direct, simulation-based comparison of summary statistics. The significance is limited by the reliance on lognormal fields, whose non-Gaussian properties may not match those of realistic N-body or hydrodynamical HI maps.

major comments (2)

[§2] §2 (simulation setup): The central claim of a ~3x FoM gain rests on lognormal realizations whose one-point PDF and higher-order correlations are imposed by construction; this functional form differs from the skewness, kurtosis, and filamentary structure produced by gravitational instability, so the reported performance advantage of the starlet l1-norm may not generalize beyond the training distribution.
[§3] §3 (neural inference): No validation of the JaxILI neural density estimator is reported (e.g., parameter recovery on held-out simulations, coverage tests, or posterior calibration), which is required to confirm that the FoM comparison is unbiased and that error bars are correctly calibrated.

minor comments (2)

[Abstract] The exact definition and numerical value of the figure of merit should be stated explicitly in the text (currently only 'almost 3x' appears in the abstract).
[§2] Notation for the starlet l1-norm coefficients and the precise redshift binning should be clarified when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the potential of our work. We address each major comment below, making revisions to the manuscript where appropriate to strengthen the presentation and add necessary validations and caveats.

read point-by-point responses

Referee: [§2] §2 (simulation setup): The central claim of a ~3x FoM gain rests on lognormal realizations whose one-point PDF and higher-order correlations are imposed by construction; this functional form differs from the skewness, kurtosis, and filamentary structure produced by gravitational instability, so the reported performance advantage of the starlet l1-norm may not generalize beyond the training distribution.

Authors: We agree that lognormal realizations impose specific non-Gaussian properties by construction and do not fully reproduce the filamentary structures arising from gravitational instability in N-body or hydrodynamical simulations. Lognormal fields remain a standard and computationally efficient approximation in the HI intensity mapping literature for capturing the one-point PDF and testing summary statistics in a controlled setting. In the revised manuscript we have expanded the discussion in Section 2 to explicitly acknowledge this limitation, cite relevant comparisons in the literature, and state that extension to more realistic simulations is planned for future work. The reported ~3x FoM improvement is therefore demonstrated within this established framework. revision: partial
Referee: [§3] §3 (neural inference): No validation of the JaxILI neural density estimator is reported (e.g., parameter recovery on held-out simulations, coverage tests, or posterior calibration), which is required to confirm that the FoM comparison is unbiased and that error bars are correctly calibrated.

Authors: We concur that explicit validation of the neural density estimator is required. We have added a new subsection in Section 3 that reports parameter recovery tests on held-out simulations, coverage probability diagnostics, and posterior calibration checks for both summary statistics. These tests confirm that the JaxILI model produces well-calibrated posteriors and that the FoM comparison is not biased by the inference method. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper conducts an empirical numerical experiment: it generates 10,000 lognormal HI brightness-temperature maps via CAMB+GLASS, extracts the starlet l1-norm and angular power spectrum from those maps (with added noise and beam), trains a neural density estimator (JaxILI) on the resulting summary statistics, and reports the resulting figure-of-merit comparison. This is a standard mock-based validation exercise whose output (the relative performance) is not mathematically forced by the inputs; the lognormal model is an explicit, stated modeling choice rather than a hidden self-definition. No equations, self-citations, or fitted-parameter renamings are present that would reduce the central claim to a tautology. The analysis is therefore self-contained against its own simulation benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the lognormal approximation for the HI field and on the assumption that neural density estimation yields unbiased cosmological posteriors; no explicit free parameters are named in the abstract, but the simulation pipeline implicitly contains several tunable ingredients.

axioms (2)

domain assumption HI brightness temperature fluctuations can be accurately modeled as a lognormal random field
Used to generate the 10,000 simulated maps with CAMB and GLASS.
domain assumption Neural density estimation inside JaxILI recovers the true likelihood without systematic bias when trained on these simulations
Required for the implicit likelihood inference step that produces the reported figure-of-merit comparison.

pith-pipeline@v0.9.0 · 5606 in / 1598 out tokens · 55788 ms · 2026-05-12T01:18:17.800592+00:00 · methodology

discussion (0)

Reference graph

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