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REVIEW 4 major objections 6 minor 61 references

Filtering out large-scale noise for cluster weak-lensing mass estimation

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Wiener filtering the observed galaxy density field removes large-scale noise from cluster weak-lensing mass estimates.

desk verdict A credible, honest methods paper on Wiener filtering for stacked cluster magnification masses whose main validation gap — the forward model shares the filter's noise model — is real and fixable. read the letter →

arxiv 2505.13399 v1 pith:VJWSUDI2 submitted 2025-05-19 astro-ph.CO

C. Murray , C. Combet , C. Payerne , M. Ricci This is my paper · ORCID
classification astro-ph.CO
keywords weak-lensingmagnificationgalaxyclustermassesWienerfilternoisecovariancecosmicvarianceHyperSuprime-CamCAMIRAclustersNFWprofile
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Cluster masses inferred from weak-lensing magnification are limited by noise that is spatially correlated across the survey, so simple radial averaging is not optimal. This paper introduces a Wiener filter that downweights the large-scale modes of the observed galaxy density field before measuring stacked magnification profiles, using the cluster NFW convergence profile as the signal prior and a noise power spectrum measured from random sky positions. Applied to 1155 CAMIRA clusters in the Hyper Suprime-Cam survey, the filter removes most of the correlation between radial magnification bins while leaving the estimated mass consistent with the unfiltered measurement. The authors argue that because the residual error is currently dominated by irreducible shot noise, the benefit is modest with HSC data but will grow for deeper surveys; the same technique applies to weak-lensing shear.

What carries the argument

The Wiener filter, Eq. (25): each Fourier mode of the observed galaxy density field is rescaled by $\hat{\kappa}_{\ell m} = \frac{C^{\kappa}_{1h,\ell}}{C^{\kappa}_{1h,\ell}+C^{n}_{\ell}} d_{\ell m}$, where $C^{\kappa}_{1h,\ell}$ is the angular power spectrum of the NFW convergence profile (the signal prior, with small scales below 2 arcminutes downweighted) and $C^{n}_{\ell}$ is the noise power spectrum estimated by averaging 2D power spectra from 10,000 random sky positions. The filter removes both low-$\ell$ modes from large-scale structure along the line of sight and high-$\ell$ shot-noise-dominated modes. Because the filter changes the shape of the magnification profile, the paper forward-models filtered profiles from simulated noisy fields so that the mass estimate is unbiased.

What would settle it

Take the same 1155 clusters, measure their stacked shear profile (whose noise is largely independent of the magnification shot noise), and compare the shear-inferred mass to the filtered-magnification mass; a disagreement beyond the statistical error would indicate that the filter's noise model is wrong. A more direct test is to check that the filtered profiles around the 10,000 random positions have zero mean and that the empirical noise power measured at cluster positions matches the random-position estimate.

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Extended reading notes

Core claim

The central claim is that Wiener filtering the observed magnification field, weighting each Fourier mode by the ratio of the NFW one-halo signal power to the total signal-plus-noise power, produces a stacked cluster magnification profile whose radial bins have substantially lower noise correlations than unfiltered profiles, with no loss of constraining power. The paper demonstrates this in two ways: simulated magnification fields show a clear reduction in off-diagonal covariance, and HSC data show the same effect. Mass estimates from filtered and unfiltered fields are consistent (log10 M/Msun = 14.10+0.15-0.22 vs 14.20+0.17-0.30), with the filtered posterior slightly tighter. The method is presented as a simplification of a full field-level maximum-a-posteriori estimate, and the authors emphasize that forward-modelling the filtered profile is required to avoid bias.

Load-bearing premise

The noise power spectrum measured from 10,000 random positions is an unbiased, stationary, Gaussian description of the noise at the cluster positions; if it is not, the filter will not remove the right modes and the forward-modelled mass estimate could be biased.

Editorial extensions

If this is right

  • Noise correlations between radial magnification bins are significantly reduced by the filter, making the stacked signal closer to a diagonal-covariance measurement.
  • Filtered and unfiltered mass estimates agree, so the method adds no detectable bias at the current precision.
  • For deeper surveys with smaller shot noise, the relative improvement in mass uncertainty should grow because the correlated large-scale noise becomes the dominant error.
  • The same Wiener filter construction is directly applicable to weak-lensing shear fields.
  • Because the filter suppresses large-scale survey modes, it can relax requirements on survey uniformity for magnification-based mass estimates.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the method scales to individual clusters rather than stacks, it could turn the mass-richness relation itself into a field-level estimate, which the paper sketches in Sect. 3.2 but does not implement.
  • The filter's signal prior is derived from an NFW profile with a fixed concentration; allowing the prior to vary with richness or redshift might recover some of the two-halo signal that the current filter removes, at the cost of reintroducing covariance.
  • The testable prediction that deeper surveys will see larger gains could be checked by running the same pipeline on simulated deep surveys before real data arrive.
  • If dust extinction is non-negligible, the magnification response R differs by band; the filter would then need a multi-band extension, which the paper identifies but does not pursue.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a Wiener-filtering method for cluster weak-lensing magnification maps, intended to remove spatially correlated large-scale noise before radial averaging. The filter is constructed from an NFW-based signal prior and a noise power spectrum estimated from random positions, and it is applied to 1-degree patches around 1155 CAMIRA clusters in HSC. The authors show that the filtered maps have substantially reduced off-diagonal radial-bin noise correlations, that the filtered and unfiltered stacked mass estimates are consistent (log10 M/M_sun = 14.10+0.15-0.22 vs 14.20+0.17-0.30), and that the filtered errors are slightly smaller. They argue that for deeper surveys, where shot noise is less dominant, the method will yield larger improvements.

Significance. If validated, this would be a useful and fairly general technique for suppressing large-scale structure noise in stacked cluster lensing measurements, applicable to both magnification and shear. The covariance formalism in Sect. 3.1 is standard, and the qualitative claim that Wiener filtering reduces radial-bin noise correlations is convincingly demonstrated in both idealized simulations (Fig. 3) and HSC data (Fig. 7). The HSC measurement is internally consistent, and the background selection and convergence-response treatment in Sect. 4 are careful. The main weakness is that the unbiasedness of the filtered mass estimate is not yet established: the forward model in Sect. 6 is unvalidated and shares its noise model with the filter, so the central methodological claim rests on an unproven condition. The projected improvement for deeper surveys is also not quantitatively supported by the simplified simulations.

major comments (4)
  1. [§6, Eq. (35)] The unbiasedness claim for the filtered mass estimate rests on the sentence: "This forward-modelling approach means that our mass estimation is not biased, provided our noise model describes accurately the observed data." This condition is never demonstrated. The noise power spectrum estimated in §5.1 is used both to construct the Wiener filter (Eq. 25) and to generate the noisy fields in the forward model, so any error in that spectrum affects the filtered data and the filtered model coherently; agreement between filtered and unfiltered masses in §6 is therefore not a test of the noise model. The mock fields in §3.4 are Gaussian, omit the two-halo term, and do not include the real survey mask, and the authors themselves describe quantitative forecasts from them as "overly optimistic." I would need an end-to-end recovery test, in which clusters of known mass are injected into realistic masked HSC-like fields and the full filtered pipeline is run, to support the central claim of unbiased mass estimation.
  2. [§5.1 and §2.2] The noise power spectrum is estimated by averaging over 10,000 random positions in the survey, but the filter is then applied to patches centered on CAMIRA clusters. Cluster positions are biased tracers of large-scale structure, so the noise at those positions includes the correlated two-halo environment described in §2.2 and possibly residual cluster-member contamination; the random-position average does not obviously capture these contributions. Because the same spectrum enters both the filter and the forward model, a cluster-environment-dependent error in the noise model is precisely the kind of systematic that would bias the filtered mass without producing a filtered/unfiltered inconsistency. A direct comparison of the power spectrum measured at cluster positions with the random-position estimate, or an explicit quantitative argument that the difference is negligible, is needed.
  3. [§3.3, Eqs. (24)-(25)] The signal prior C1h is defined as the Fourier transform of an NFW convergence profile, but the paper does not specify the mass, concentration, and redshift (or stacking distribution) used to construct it, nor the exact procedure for setting the sub-2-arcmin region to 10^-5. The Wiener filter, and therefore the filtered data and the forward-modeled profiles, depends on these unspecified choices. A sensitivity test over a plausible range of NFW prior parameters and downweight scales is required to show that the mass estimate and the claimed error reduction are robust to this prior.
  4. [§3.4 and §7] The conclusion that the error reduction will become larger with future deeper datasets is stated in the abstract and conclusions, but the only quantitative support is the simplified simulation of §3.4, which the authors explicitly caution would yield "overly optimistic" forecasts. No forecast is made with an HSC-like noise amplitude, source density, mask, or cluster redshift distribution. This claim should either be supported by a more realistic end-to-end simulation or softened to a qualitative expectation.
minor comments (6)
  1. [§3.2, Eqs. (20)-(21)] The Gaussian likelihoods are missing the factor -1/2 and the transpose in the exponent; as written, exp[(d_i - kappa_i) C^-1 (d_i - kappa_i)] is not a correctly normalized Gaussian exponent.
  2. [§4.2] The sentence "We also employed a magnitude cut on the i-band magnitude with 23.5 < i" appears to have the inequality reversed; the text and Fig. 5 indicate the intended cut is i < 23.5.
  3. [§3.2] The phrase "not in the least because" should likely read "not least because" in the discussion of why estimating many cluster parameters is non-trivial.
  4. [§3.1, Eq. (18)] The subscript notation on C^n_total is inconsistent with the terms on the right-hand side, which all carry (i,j); the total covariance should be written C^n_total,ij, and the terms C^ulss_ij and C^clss_ij should be defined before or immediately in the equation.
  5. [§6] The text refers to "six linearly spaced angular bins between 0.75 and 5.2 Mpc," mixing angular and physical units; the conversion using the mean cluster redshift should be stated explicitly to avoid ambiguity.
  6. [References] The reference list contains two entries for Umetsu et al. 2014 with identical bibliographic data; one should be removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Wiener filter uses a fixed NFW signal prior and a noise spectrum measured from random positions, and the cluster mass is not an input to the filter.

full rationale

The derivation chain is self-contained against external data (HSC galaxies and CAMIRA clusters) and does not reduce to its own inputs. The Wiener filter (Eq. 25) is built from two fixed ingredients: a signal prior C_{1h} obtained by Fourier-transforming the NFW convergence profile (Eq. 9) and a noise power spectrum estimated from 10,000 random positions (Sect. 5.1). Neither ingredient is fitted to the cluster mass being estimated; the likelihood (Eq. 35) then varies log10M against the measured stacked profiles. The filtered-field model is forward-modelled by applying the same filter to simulated noisy fields generated from the observed noise spectrum, so the filter's effect on the profile shape is accounted for rather than treated as an extra fitted parameter. The quoted conditionality, 'provided our noise model describes accurately the observed data' (Sect. 6), is an explicit assumption; if the noise model is wrong the filtered and unfiltered estimates could share a common bias, but that is a validation or systematic-error concern, not an equivalence of output to input by construction. The only self-citation (Murray et al. 2022) appears in a list of shear mass-estimation examples and is not load-bearing. Claims about reduced bin-to-bin noise correlations are checked with bootstrap covariances of the actual cluster profiles (Fig. 7), not assumed from the filter construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The filter's derivation rests on standard weak-lensing equations and assumed power spectra; the main inputs the paper supplies are the choice of C1h from NFW and the noise estimate from random positions. No new physical entities are introduced.

free parameters (3)
  • Convergence response R = 1.54
    Measured from the HSC galaxy sample by modulating magnitudes and applying selection (Sect. 4.3); converts galaxy overdensity to convergence. It is an empirical calibration, not fitted to the mass estimate, but it propagates into all magnification profiles.
  • Signal prior NFW parameters for C1h = unspecified
    The Wiener filter in Eq. 25 uses C1h from the NFW profile (Sect. 3.3). The fiducial mass and concentration used to compute this prior are not stated, so the filter's scale selection is not fully reproducible.
  • Small-scale downweight threshold in C1h = <2 arcmin set to 1e-5
    Sect. 3.3: the central region of the NFW prior is manually set to 1e-5 to downweight small scales; this choice shapes the filter and affects the filtered profiles.
assumptions (5)
  • domain assumption Cluster dark matter halos are well described by the NFW profile.
    Used throughout for the one-halo lensing signal (Eq. 9-10) and for the signal prior C1h (Eq. 24).
  • domain assumption The noise in the magnification field is approximately Gaussian and stationary.
    Used to justify the Gaussian likelihood (Eq. 20) and Wiener filter (Eq. 25); the paper acknowledges this is approximate at small scales (Sect. 7).
  • domain assumption The galaxy angular power spectrum Cgg and the source redshift distribution are sufficient to model the noise covariance.
    Eq. 15 uses Cgg with a Gaussian source redshift distribution at z=1.4, sigma=0.4/sqrt(2pi) for the analytic covariance; assumed in Fig. 2 and simulations.
  • domain assumption The mass-concentration relation (Dutton & Maccio 2014) and halo bias relation (Tinker 2010) are correct.
    Fixed in the mass estimation (Sect. 6) to break degeneracies.
  • domain assumption The colour-cut source selection removes cluster member contamination and the measured convergence response R is applicable.
    Sect. 4.2; Fig. 4 shows the colour-cut sample has a clean magnification signal, but member contamination cannot be fully ruled out.

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Cite this review

Pith. "Pith review of Filtering out large-scale noise for cluster weak-lensing mass estimation." pith.science (2026). https://pith.science/paper/VJWSUDI2

@misc{pith2026250513399,
  author       = {Pith},
  title        = {Pith review of: Filtering out large-scale noise for cluster weak-lensing mass estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJWSUDI2}},
  note         = {Machine review of arXiv:2505.13399}
}
read the original abstract

We present a new method for estimating galaxy cluster masses using weak-lensing magnification. The effect of weak-lensing magnification introduces a correlation between the position of foreground galaxy clusters and the density of background sources. Therefore, cluster masses can be inferred through observations of these correlations. In this work, we introduce a method that allows us to considerably reduce noise correlations between different radial bins of the cluster magnification signal via a Wiener filtering of our observed magnification field on large scales. This method can reduce the uncertainty on the estimated galaxy cluster mass and it can also be applied to cluster mass estimation for weak-lensing shear. The method was applied to Hyper-Suprime Cam galaxies and CAMIRA clusters detected within the Hyper-Suprime Cam survey (HSC). With HSC data, we find that our filtering method significantly reduces the correlation of noise between radial magnification bins. The estimated cluster mass is consistent between the filtered and unfiltered methods, with similar errors between the two methods as our current measurement errors contain significant contributions from the irreducible shot-noise. For deeper surveys, the effects of shot noise will be less important and this method will lead to greater improvements on the estimated cluster mass.

Figures

Figures reproduced from arXiv: 2505.13399 by the authors.

Figure 1
Figure 1. Illustration of a circular region of a mock galaxy density field, where we consider a circular annulus about a central point. This is a Gaussian noise random field generated from the galaxy angular power spectrum, introduced in Sect. 3. measurements to be largely independent and provide an impor￾tant systematic check upon one-another. Weak-lensing magnification has been used to measure galaxy cluster masses in many … view at source ↗
Figure 2
Figure 2. The noise covariance between radial bins as a function of the minimum ℓ used for the integration in Eq. 15. This shows how different multipoles contribute to the radial covariance. θi , θj refer to the radial bins used to compute the covariance. The figure shows both the diagonal and off-diagonal terms in the covariance. In the following, we consider the covariance between radial bins of width 1 arcminute. Top: Elem… view at source ↗
Figure 3
Figure 3. Top: Radial correlation matrix for the Wiener filtered field. Bot￾tom: Radial correlation matrix for the unfiltered field. For both fields the galaxy density is Ngal = 20 per square arcminute. Note: the cor￾relation matrices are limited between 0 and 1 (instead of between −1 and 1) to see the difference between the two correlation matrices more clearly. Here, the radial bins are linearly spaced bins between 0 and 10… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Normalised magnitude distributions for two different back￾ground galaxy sample selections. We compare the magnitude distribu￾tion of galaxies in the field as compared to those within the fields of galaxy clusters. Field galaxies are from random points within the sur￾ve…
Figure 5
Figure 5. Figure 5: Response of the galaxy sample to the change in galaxy mag￾nitudes from magnification and dilution. The solid lines are calculated with Eq. 32 and the dashed lines are calculated using Eq. 4 and the ap￾proximation used in Eq. 32 . The dashed black line shows the magnitu…
Figure 7
Figure 7. Figure 7: We see that the filtered fields significantly reduce corre￾lations between the different angular bins of the cluster magnifi￾cation profiles. 0 2 4 6 8 10 R bins 0 2 4 6 8 10 R bins 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 R bins 0 2 4 6 8 10 R bins 0.0 0.2 0.4 0.6 0.8 1.0…
Figure 8
Figure 8. Figure 8: Posteriors of the mass-estimation for our filtered and unfiltered approach. The posteriors are estimated from the MCMC chains. radius limit was set to avoid the effects of cluster miscentering and higher foreground galaxy contamination in our magnifica￾tion profiles. T…

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Reviewed August 15, 2026 · model on record in the stance chip above.