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REVIEW 4 major objections 3 minor 103 references

AMICO-WL: an optimal filtering algorithm for galaxy cluster detections with weak lensing

T0 review · 4 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper introduces AMICO-WL, an optimal matched-filter cluster detector for weak-lensing data, and shows that cutting foreground galaxies at redshift 0.2 doubles completeness at 70% purity on Euclid-like mock data.

desk verdict A solid, honestly reported matched-filter weak-lensing cluster finder with a clever simulation-side matching tool; the headline completeness gain is real but conditional on exact redshifts and a single mock realization. read the letter →

arxiv 2501.16420 v1 pith:2XXYJU66 submitted 2025-01-27 astro-ph.CO

Leonardo Trobbiani , Matteo Maturi , Carlo Giocoli , Lauro Moscardini , Gabriele Panebianco This is my paper · ORCID
classification astro-ph.CO
keywords weakgravitationallensinggalaxyclustersoptimalmatchedfilterforegroundremovalEuclid-likemockcataloguespurityandcompletenessclusterdetectioncosmicshearnoise
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

Weak-lensing cluster detection traces all matter, not just baryons, so the paper extends the AMICO optimal matched-filter cluster finder to work on galaxy ellipticities instead of galaxy overdensities. The paper's central claim is that removing foreground galaxies with a redshift cut at $z_{\min}=0.2$ makes the detector substantially more efficient: on a 25 square-degree Euclid-like mock field, at 70% purity completeness doubles from 6.5% to 13.0% while spurious detections decrease. This matters because upcoming wide surveys such as Euclid will measure the shapes of billions of galaxies, and a pure, complete weak-lensing cluster sample would complement optical, X-ray, and SZE selection with a mass-based selection independent of baryonic emission.

What carries the argument

The load-bearing object is the linear optimal matched filter $\Psi$, defined in Fourier space as $\hat{\Psi}(k)\propto \hat{\tau}(k)/P_N(k)$, where $\hat{\tau}$ is the Fourier transform of the assumed Navarro-Frenk-White tangential-shear profile and $P_N=P_\epsilon+P_\gamma$ is the noise power spectrum combining shape noise and the cosmic-shear power spectrum from non-linear structure growth. The filter is applied to the tangential ellipticities of galaxies to build an amplitude map, and detections are peaks in the signal-to-noise map. Around that core the paper adds a foreground-removal redshift cut with re-optimised filter parameters, a signal-to-noise threshold calibrated by comparing positive and negative E-mode peaks so that the desired sample purity can be set in advance, and an iterative cleaning step that subtracts the filtered shear model of each detection before searching for the next peak. Performance is assessed with a lens-plane 'blinking' matching procedure that removes one $\Delta z=0.1$ matter slice at a time, giving each detection a redshift anchor.

What would settle it

Re-run the FR02 and COMPLETE configurations on a mock that assigns photometric-redshift scatter $\sigma_z/(1+z)\simeq 0.05$ to the galaxy redshifts before applying the $z_{\min}=0.2$ cut; if the FR02 completeness advantage over COMPLETE at 70% purity does not remain significant, the headline gain does not transfer to real survey data.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a simple pre-processing step—cutting every galaxy whose true redshift lies below $z_{\min}$ out of the shear catalogue and re-optimising the filter for the truncated catalogue—transforms a weak-lensing cluster finder into one whose completeness at fixed purity roughly doubles, from 6.5% to 13.0% at 70% purity, while reducing spurious detections. The paper attributes the gain to removing the noise contribution of galaxies in the foreground of the target haloes, whose shapes dilute the tangential-shear signal and add variance to the maps. The paper also introduces a 'blinking' redshift-plane matching procedure that assigns redshift information to weak-lensing detections, shows that matched detections peak at lens redshifts $0.3<z<0.4$ where lensing efficiency is maximum, and classifies the remaining spurious detections into noise fluctuations, chains of low-mass haloes aligned along the line of sight, and structures missed by the reference halo mass cut.

Load-bearing premise

The load-bearing premise is that every galaxy in the input catalogue has an exact, error-free redshift, so the $z_{\min}$ cut cleanly separates foreground from background; the paper states that no photometric-redshift uncertainty is included.

Editorial extensions

If this is right

  • At a fixed sample purity of 70%, applying the $z_{\min}=0.2$ foreground cut raises completeness from 6.5% to 13.0% compared with using the full galaxy catalogue.
  • The foreground cut also lowers the number of spurious detections: in the paper's taxonomy, non-vanished spurious detections fall from 17 to 6 and non-matched spurious detections from 65 to 42 in the FR02 run.
  • At the more conservative 80% purity level the completeness of the four configurations converges, because only the high signal-to-noise peaks from the most massive, best-lensed haloes survive.
  • The lens-plane blinking matching shows that detections concentrate at lens redshifts $0.3<z<0.4$, consistent with lensing geometry, and it supplies a redshift estimate that ordinary positional matching cannot give.

Reading between the lines

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

  • A testable extension would rerun the same four configurations on a mock with photometric-redshift scatter $\sigma_z/(1+z)\simeq 0.05$; the completeness gap between FR02 and COMPLETE at fixed purity is likely to shrink once the sharp $z_{\min}=0.2$ boundary is blurred.
  • Because the mock neglects source clustering, the shape-noise term $P_\epsilon$ used in the filter and the negative-peak purity calibration may underestimate correlated-noise contamination on real data; adding clustering would quantify this.
  • The purity estimator compares positive and negative E-mode peaks and assumes they share the same noise and large-scale-structure statistics; on real data, shear systematics that break E/B symmetry would require external calibration of this estimator.
  • The foreground-removal idea could be made redshift-dependent, with a cut threshold matched to each lens plane, which the paper notes as a possible development; this could push the 70%-purity completeness beyond the reported 13%.
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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 / 3 minor

Summary. The paper introduces AMICO-WL, a weak-lensing extension of the AMICO optimal matched filter code for galaxy cluster detection. The algorithm constructs E-mode and B-mode amplitude maps from galaxy ellipticities, derives SNR thresholds through a comparison of positive and negative E-mode peak statistics, and includes a cleaning procedure to handle blended detections. The method is tested on a 25 deg^2 Euclid-like mock built from the DUSTGRAIN-pathfinder simulation, using four configurations: COMPLETE and three foreground-removed runs (FR02, FR04, FR06) based on redshift cuts at z_min = 0.2, 0.4, 0.6. Detections are matched to haloes with M200 > 5e13 h^-1 Msun using a new 'blinking' procedure that removes individual redshift slices to infer the redshift of the lensing signal. The headline result is that, at ~70% purity, the FR02 run achieves 13.0% completeness versus 6.5% for the COMPLETE run, with a concurrent reduction in spurious detections.

Significance. If the headline result is robust, AMICO-WL provides a practical, well-tested weak-lensing cluster finder for Euclid, building on the established AMICO infrastructure and adding a principled SNR-threshold calibration and a novel matching technique for simulation validation. The paper is transparent about its mock assumptions and includes a careful spurious-detection taxonomy. Strengths include the use of the standard optimal filter formalism, the B-mode consistency check, the support for the matching procedure provided by the positional scatter distribution in Fig. 12, and the detailed analysis of the origin of false positives. The main risk is that the quantitative performance claims are derived under idealized assumptions—exact redshifts and no source clustering—that may not transfer to real Euclid data, and the absence of any uncertainty estimates makes it difficult to judge the significance of the reported factor-of-two gain.

major comments (4)
  1. [Sect. 3 and Sect. 4.2] The headline result (6.5% to 13.0% completeness at ~70% purity) rests on the FR02 configuration, which applies a hard redshift cut at z_min = 0.2 using the true redshifts of the mock galaxies. The manuscript states in Sect. 3 that 'we do not consider any photometric redshift uncertainty in our analysis.' Real Euclid photo-z errors, with typical scatter around sigma_z ~ 0.05(1+z), will scatter galaxies across this boundary, blurring the foreground/background separation, modifying the effective source density entering Eq. (26), and changing the LSS noise contribution in Eq. (28). This is a load-bearing simplification for the quantitative headline, and the paper should either include a photo-z error model or explicitly frame the factor-of-two gain as an idealized proof of concept rather than a Euclid-ready performance prediction.
  2. [Sect. 3 and Sect. 5.2] The mock galaxies are 'randomly distribute[d] in the map, neglecting source clustering.' The filter noise model (Eqs. 24-25) and the purity calibration based on positive/negative E-mode peak statistics (Eq. 29) assume uncorrelated shape noise and Gaussian LSS statistics. Source clustering introduces correlations in the noise field and in the peak counts, which can bias the SNR thresholds and the purity estimates. Since the paper claims the thresholding method sets a desired sample purity, a quantitative test of the sensitivity to source clustering (e.g., a clustered or log-normal source catalogue) is needed to support the validity of the purity calibration for survey-like data.
  3. [Table 2 and Sect. 6.2] The completeness and purity values are quoted without uncertainties, and all numbers come from a single 25 deg^2 mock field. In the '~70% PUR' rows of Table 2, the measured purity is not reported, only the SNR threshold, number of detections, and completeness. Because the Eq. (29) calibration is imperfect (the TOTAL row shows predicted 70% purity yielding measured purities of 61%, 71%, 64%, and 61% for COMPLETE, FR02, FR04, and FR06, respectively), the reader cannot verify that the headline 6.5% versus 13.0% comparison is actually at matched measured purity. The authors should report the measured purity in every row and provide error estimates, such as jackknife over subfields or field-to-field variance, for the completeness and purity values that support the central claim.
  4. [Sect. 5.2, Eq. (29)] The purity calibration of Eq. (29) assumes that negative E-mode peaks follow the same noise statistics as positive peaks except for the absence of cluster signals. The measured purities in the TOTAL row of Table 2 deviate from the predicted 70% by up to 9 percentage points for the COMPLETE, FR04, and FR06 runs, showing that the calibration is not accurate across configurations. This discrepancy indicates that the symmetry between positive and negative peaks is not fully realized in the simulations, and it directly affects the reliability of the SNR thresholds used to define the operating points. The calibration should be validated per configuration, or the paper should base its purity-matched comparison entirely on the measured purity rather than the predicted value.
minor comments (3)
  1. [Sect. 2.2, Eq. (20)] The notation 'averageb' appears to be a typo for 'average b', and the sentence defining the bias term is confusing; please clarify that b is the bias of the estimator and that the constraint in Eq. (20) is imposed to make it zero.
  2. [Table 1] The parameter 'white noise N_epsilon' is not defined in the table caption; please specify whether it corresponds to the power spectrum P_epsilon of Eq. (24) or to its square root, and give its units.
  3. [Sect. 7] There are typographical issues in phrases such as 'lineofsight' appearing in the text; please correct these to 'line-of-sight' throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the headline completeness and purity numbers are measured against an external halo catalogue, and the purity estimator of Eq. (29) is falsifiable (it fails for COMPLETE).

full rationale

The derivation chain is self-contained with respect to the paper's headline claims. The matched filter is derived in Eqs. (18)-(22) inside the paper, so the citations to Maturi et al. (2005, 2007) are provenance for a standard optimal-filter construction rather than an unverified premise. The purity control of Eq. (29) is an estimator based on the symmetry of positive and negative E-mode noise peaks, and it is not self-fulfilling because it is independently checked: for the COMPLETE run, the predicted 70% purity threshold yields a measured purity of only 61% (Table 2), so the estimator is falsifiable and does not reduce to its own definition. Completeness and purity in Sect. 6 are measured by cross-matching detections to the simulation halo catalogue through the lens-plane 'blinking' procedure, which is an external ground truth independent of the filter template. The foreground-removal gain (6.5% to 13.0% at roughly 70% purity) is an empirical comparison of measured completeness at calibrated thresholds, not a fitted parameter renamed as a prediction. The acknowledged simplifications, exact redshifts and neglected source clustering (Sect. 3), limit transferability to Euclid but do not make any equation reduce to its input. Self-citations are present, for the AMICO code and for the matched filter, but they are not load-bearing: the AMICO code was externally validated in the Euclid Cluster Finder Challenge, and the filter construction is reproduced in this paper. I therefore find no circular step.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper's central performance claims rest on a chain of modeling choices: template halo mass and redshifts, foreground redshift cuts, matching radii, and target purity, plus simulation assumptions such as exact galaxy redshifts, no source clustering, NFW profiles, and the single-plane blinking assumption. None of these is falsified outside the paper; they are either taken from prior literature or chosen by hand. The only independent checks are internal, the B-mode null test and the positional scatter in Fig. 12, which support the matching procedure but not the absolute completeness numbers.

free parameters (7)
  • Template halo mass M_l = 1e15 h^-1 M_sun (all runs)
    Chosen for all four filters (Table 1); sets the NFW shear profile shape in the matched filter. Not fitted to this dataset, but it controls the filter response and hence detection thresholds.
  • Template lens redshift z_l = 0.4 (COMPLETE), 0.2 (FR02), 0.4 (FR04), 0.6 (FR06)
    Set per run (Table 1); with z_s, defines the lensing efficiency and filter shape. Values are chosen by hand based on the redshift cuts.
  • Template source redshift z_s = 0.93, 0.98, 1.06, 1.18
    Effective source redshifts per filter (Table 1), taken from the source redshift distribution. Chosen, not fitted.
  • Foreground removal redshift cuts z_min = 0.2, 0.4, 0.6
    Three cuts are scanned and FR02 is reported as best. The reported doubling of completeness comes from the best of three tested cuts, a post-hoc selection that inflates the headline gain.
  • Blinking matching radii = 0.6 arcmin (vanished matching), 3 arcmin (halo matching)
    Chosen by inspecting typical peak extension in the amplitude maps (Sec 6.1). These choices directly set which detections count as vanished or matched and thus set the purity and completeness numbers.
  • Target sample purity for thresholding = 70% (also 80%)
    The SNR threshold is set to the level where Eq. (29) predicts 70% purity. The target purity is a user-chosen operating point; the achieved purity differs for COMPLETE, which reaches 61%, showing the calibration is imperfect.
  • Lens plane slice thickness = Delta z = 0.1
    Chooses the redshift resolution of the blinking procedure; affects which detections vanish and how many halos are matched. Chosen for computational practicality.
assumptions (6)
  • domain assumption The weak lensing signal of a cluster is well described by an NFW shear profile with the adopted concentration.
    Used to construct the matched filter (Sec. 4.1). If real halos deviate, the filter is suboptimal, but the detection procedure still functions.
  • domain assumption Negative E-mode peaks are generated only by noise and LSS underdensities, never by clusters.
    Sec 5.2: the purity estimator P = (E_SNR - Ehat_SNR)/E_SNR assumes cluster lensing contributes only positive peaks. Approximately true for a tangential-shear matched filter, but ignores noise-driven sign flips and mask or systematic effects.
  • domain assumption Background source redshifts are known exactly; no photometric redshift uncertainty.
    Sec 3: the galaxy catalogue uses true redshifts. Foreground removal in Sec 4.2 depends on this; real surveys have photo-z errors that will blur the z > z_min cuts and reduce the demonstrated gain.
  • domain assumption Source galaxies are unclustered; they are randomly distributed in the map.
    Sec 3: 'we randomly distribute them in the map, neglecting source clustering.' Source clustering adds noise correlations and can change peak statistics, so the purity calibration of Eq. (29) may be optimistic.
  • domain assumption Each halo's lensing signal is localized to a single Delta z = 0.1 lens plane, so removing that plane makes a true detection vanish.
    Sec 6.1: the blinking matching identifies detections as real only if they disappear when one plane is removed. Projection effects and LSS along the line of sight can cause signal loss across several planes; the paper acknowledges multiple associations.
  • domain assumption Born approximation and multi-plane ray tracing through 27 lens planes accurately reproduce weak lensing in the light-cone.
    Sec 3: MapSim uses the Born approximation and has been validated at per-cent level for peak statistics against other algorithms (Hilbert et al. 2020).

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Cite this review

Pith. "Pith review of AMICO-WL: an optimal filtering algorithm for galaxy cluster detections with weak lensing." pith.science (2026). https://pith.science/paper/2XXYJU66

@misc{pith2026250116420,
  author       = {Pith},
  title        = {Pith review of: AMICO-WL: an optimal filtering algorithm for galaxy cluster detections with weak lensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2XXYJU66}},
  note         = {Machine review of arXiv:2501.16420}
}
abstract

The detection of galaxy clusters, the most massive bounded structures in the universe, is crucial for cosmological analysis. Weak lensing signals allow us to track the distribution of all (dark and baryonic) matter regardless of its observable electromagnetic properties. Upcoming wide-field surveys like Euclid and LSST-Rubin will provide enhanced shape measurements of billions of background galaxies, presenting an unparalleled opportunity to detect galaxy clusters on a vast cosmic scale. The immense data volume generated by these surveys will require efficient and accurate analysis techniques. In this work, we introduce AMICO-WL, an extension of the optimal filtering algorithm implemented in AMICO, a well-tested code developed for optical cluster detection. AMICO-WL implements a specific linear optimal matched filter for weak lensing data in the AMICO infrastructure, using parallelisation and adding an efficient signal-to-noise ratio thresholding approach to set a desired sample purity and a cleaning procedure to deal with blended detections. The algorithm has been tested on a 25 deg$^2$ field of Euclid-like mock galaxy catalogue with the simulated shear signal produced using DUSTGRAIN-$pathfinder$ past-light-cones. We implemented a foreground removal procedure based on different cuts of low redshift galaxies from the input catalogue. To evaluate the performance of the method, we used an efficient matching procedure based on the 'blinking' of the simulation's individual redshift lensing planes. Cross-matching the AMICO-WL detections with the dark matter halo sample in the simulation having $M_{200} > 5 \times 10^{13}$ $M_{\odot}/h$ and considering a purity level of $\sim70\%$, the application of the foreground removal doubles the completeness from $6.5\%$ to $13.0\%$ and at the same time produces a significant decrease of spurious detections.

Figures

Figures reproduced from arXiv: 2501.16420 by the authors.

Figure 1
Figure 1. Convergence map (5 deg on a side) for fixed source redshift [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Redshift distribution of the weak lensing simulated [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Reconstructed convergence map from the source redshift distribution catalogue. The left panel refers to the full light-cone [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Radial profiles (in real space) of the optimal filters em [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: The E-mode amplitude and its variance lensing signal maps are shown in the top-left and bottom-left panels, respectively, while the B-mode amplitude and its variance lensing signal maps are shown in the top-right and bottom-right panels. The maps cover a field of view …
Figure 6
Figure 6. Figure 6: S NR threshold determination analysis. Top panel: cumu￾lative S NR distributions of positive (ES NR) and absolute nega￾tive peaks (Eˆ S NR) in the E-mode map detected with SExtractor. Bottom panel: difference in cumulative counts of positive and negative peaks as a fun…
Figure 8
Figure 8. Figure 8: Distribution of signal-to-noise ratio [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 7
Figure 7. Figure 7: Example of the cleaning procedure on a 0.36 deg [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 11
Figure 11. Figure 11: Fraction (in percentage) of detections in the primary [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 10
Figure 10. Figure 10: Redshift (top panel) and virial mass (bottom panel) dis [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 12
Figure 12. Figure 12: Distribution of the scatter in position between the halo [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: Completeness as a function of purity for di [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]
Figure 14
Figure 14. Figure 14: The sample completeness in two-dimensional bins of redshift and virial mass of the matched haloes for the COMPLETE [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 15
Figure 15. Figure 15: Fraction of spurious detections as a function of [PITH_FULL_IMAGE:figures/full_fig_p014_15.png]

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