Pith. sign in

REVIEW 4 major objections 5 minor 42 references

Breaking the degeneracy in stellar spectral classification from single wide-band images

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A PSF-aware classifier recovers stellar spectral classes from single wide-band images by comparing each star to an approximate chromatic PSF model.

desk verdict Genuinely new PSF-aware classification idea with mostly honest body text, but the 91% headline is the perfect-PSF ceiling and no experiment touches model misspecification; worth serious review. read the letter →

arxiv 2501.16151 v1 pith:JPTIKLNV submitted 2025-01-27 astro-ph.IM

Ezequiel Centofanti , Samuel Farrens , Jean-Luc Starck , Tobias Liaudat , Alex Szapiro , Jennifer Pollack This is my paper · ORCID
classification astro-ph.IM
keywords stellarspectralclassificationenergydistributionchromaticpointspreadfunctionwide-bandimagingsupportvectormachinesimilarityfeaturesWaveDiffPSFmodelweakgravitationallensing
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

Stars in wide-field survey images are unresolved, so their apparent shape is the telescope's point spread function (PSF) blurred by the star's spectrum. This paper claims that a classifier can recover the spectral class of such stars from a single wide-band image if it is given a preliminary model of how the PSF varies with wavelength. The method computes similarity features between the observed star and monochromatic PSF predictions at eight wavelengths and feeds them to a support vector machine. On simulated Euclid-like images it reaches 91% top-two accuracy with a perfect PSF, surpassing pixel-only classifiers that ignore the PSF's spectral variation. The payoff is practical: assigning spectral templates to thousands of stars without spectroscopy would enlarge the sample available for chromatic PSF modelling in weak-lensing surveys.

What carries the argument

The load-bearing object is the similarity feature vector of Eq. 4: for each wavelength bin $\lambda_k$, one minus the squared Frobenius distance between the observed star image and the approximate monochromatic PSF at that wavelength, normalized so the eight features sum to one. Because the true star image is a sum of monochromatic PSFs weighted by the SED (Eq. 2), high similarity at a wavelength marks a large SED weight, so the vector acts as a proxy for the star's spectrum. The classifier is a C-support vector machine with radial-basis-function kernels applied to these feature vectors. The authors adopt the WaveDiff PSF model both as the simulator generating ground-truth observations and as the approximate PSF model fitted to subsets of the stars, and the eight-bin SED discretization comes from Pickles templates restricted to the Euclid VIS passband.

What would settle it

Take a set of Euclid-like single-band star images with spectroscopically known spectral types, fit an approximate PSF model independently of the truth, apply the similarity-feature SVM, and compare predicted and known classes; if the top-two accuracy on such real data does not exceed the pixel-only baseline, the central claim fails. A sharper simulation test generates ground-truth observations with a PSF simulator different in family from WaveDiff and then fits the approximate model with WaveDiff; if class separation degrades sharply, the reported gains depend on using the same model family for truth and approximation.

Watch

Extended reading notes

Core claim

The central claim is that the degeneracy between PSF size and spectral type, the reason pixel-only classifiers stall around 75% top-two accuracy, can be broken by supplying the classifier with an approximate chromatic PSF model evaluated at the star's field position. In the discrete observation model, the star image is a sum of monochromatic PSFs weighted by the star's SED; the paper's similarity features measure, at each of eight wavelengths, how much the observation resembles the corresponding monochromatic PSF, normalized across wavelengths. These features act as a proxy for the SED weights, and an SVM with an RBF kernel trained on them assigns one of 13 Pickles spectral classes. With the ground-truth PSF the method reaches 91% top-two accuracy; with approximate WaveDiff PSF models the paper reports 88.6% top-two accuracy from 1000 training stars (0.9% relative error) and about 76% from 50 stars (2.4% error), and it concludes that even PSF models too coarse for weak-lensing analyses carry enough spectral information to outperform pixel-only classifiers.

Load-bearing premise

The approximate chromatic PSF model must be accurate enough, and close enough in family to the true PSF, that the similarity features separate stellar classes; in these simulations the true and approximate PSFs are both WaveDiff models, making the model family perfectly matched, and a 2.4% relative PSF error already drops top-two accuracy to about 76%, where the advantage over pixel-only methods nearly disappears.

Editorial extensions

If this is right

  • Pixel-only classification does not improve when PCA is replaced by a CNN, which the paper reads as evidence that the PSF-size/spectral-type degeneracy, rather than feature extraction, caps accuracy.
  • Approximate PSF models with 1% relative error recover 87% top-two accuracy, so the classifier does not require a final lensing-grade PSF to be useful.
  • In the proof-of-concept, adding 2,000 stars with classified SEDs to 50 stars with known SEDs reduces the PSF relative error from 2.5% to 0.78%, a reduction of almost 70%, approaching the ideal case of 2,000 stars with known SEDs.
  • The paper expects the method to work with any PSF modelling method that captures spectral variation, not just WaveDiff.

Reading between the lines

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

  • The margin shown at 2.4% PSF error suggests that on real data the gain could be fragile: if the real PSF departs from the model family, the similarity features could lose their class-discriminating power even when the PSF error is small by the paper's metric.
  • Because the similarity features are continuous proxies for the SED weights, the same pipeline could be extended to regress effective temperature or other continuous stellar parameters instead of choosing among 13 discrete templates.
  • A single-pass pipeline underestimates the method's possible value: classification and PSF fitting could be alternated so that improved PSF models yield better features and better classifications in the next round; the paper only demonstrates one pass.
  • In a real survey, the flat distribution of stellar types used here inflates accuracy relative to a magnitude-limited field where red stars dominate, so rebalancing or class-weighted evaluation would change the headline number.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript addresses the problem of assigning spectral templates to unresolved stars observed in a single wide band, motivated by chromatic PSF modelling for weak-lensing surveys. The proposed classifier forms a vector of similarity features by comparing the observed star stamp with monochromatic PSFs from a preliminary PSF model at eight wavelengths, then applies an SVM in that feature space. The method is evaluated on WaveDiff-simulated Euclid-like images against two pixel-only baselines (PCA+MLP, following Kuntzer et al. 2016, and a CNN+MLP variant). The reported top-two accuracies are 0.91 with the ground-truth PSF, 0.886 with the best approximate PSF (2000 training stars), and 0.755 with the least accurate approximate PSF (50 stars). A proof-of-concept experiment shows that adding stars classified by this method can reduce the PSF relative error from about 2.4% to 0.78%.

Significance. If the result transfers to real data, the method would be a practical way to multiply the number of SED-labelled stars available for chromatic PSF modelling in Euclid-like exposures, which is a genuine bottleneck for data-driven PSF extraction. The paper's strengths are the clear problem formulation, the use of a public, physically motivated simulator, the public implementation, and the direct comparison with two relevant baselines. However, the significance is currently limited by the fact that the evidence is entirely simulated within the WaveDiff model family; the abstract's headline 91% is a perfect-PSF upper bound, and the claimed advantage over pixel-only methods is not demonstrated in the regime of largest PSF error. I would regard the central idea as promising and worth publishing after the internal-validity issues are addressed.

major comments (4)
  1. [§5.1, §6.3.1, Table E.1, Appendix C] The entire evaluation stays inside the WaveDiff parametric family: the ground-truth PSF is generated by WaveDiff (§5.1) and every approximate model is a WaveDiff fit to WaveDiff-simulated stars (Appendix C, §6.3.1). Consequently the approximate models differ from the truth only through a smaller number of training stars; no model misspecification (wrong Zernike order, wrong spatial polynomial degree, wrong chromatic dependence, or a non-parametric component outside the parameterization) is tested. This is load-bearing because this family match is what makes the similarity features informative. At the only point where the approximate PSF is poor (S1, 2.4% relative error), Table E.1 reports top-two accuracy 0.755, essentially equal to PCA+MLP (0.757) and CNN+MLP (0.746); absent uncertainty intervals these numbers are indistinguishable. The 91% figure in the Abstract is obtained with the ground-truth PSF. I recommend adding a misspecification experiment—for example, fitting a deliberately reduced WaveDiff model to data generated with a higher-order or non-parametric perturbation—or explicitly restricting the claims to the same-family regime.
  2. [§6.3.2, Table E.1] No uncertainty quantification is reported for the classification metrics. Every accuracy/F1/top-two value is a point estimate computed on a single 1000-star test set from one random PSF field. This matters not only for the headline claims but for the detailed comparison: the difference between S1 and the pixel-only baselines is 0.2–0.9 percentage points in top-two accuracy, and the claim in §6.3.2 that the method outperforms both baselines 'for every considered error level' cannot be supported without error bars. Please provide bootstrap confidence intervals over test stars or (better) variance over several independent simulated PSF fields.
  3. [§4.2, Eq. (4)] The sentence 'The resulting similarity features serve as a proxy for the SED values b_k' is asserted rather than derived. Equation (4) is a normalized distance that is not obviously equivalent to the SED weights in Eq. (2); its informativeness depends on the PSF model and on noise. Since the whole method rests on these features, the paper should either provide a short derivation linking Eq. (4) to Eq. (2) under stated assumptions, or include an explicit validation (e.g., correlation between the feature vector and the true b_k, or classification performance when the true SED is used as the feature vector).
  4. [§6.3.3] The proof-of-concept PSF-improvement experiment is partly circular: the 2000 additional stars are assigned SED templates by a classifier that uses the same approximate PSF model that is later refined with those labels. Because the observations and the classifier both come from the WaveDiff family, the errors in the labels are correlated with the model error, so the reported drop from 2.4% to 0.78% is a self-consistency result rather than an external validation of the improvement. The text itself calls the test 'highly idealised' (§6.3.3); the conclusions section should carry the same caveat when stating that classified stars reduce the PSF error by almost 70%.
minor comments (5)
  1. [Abstract] The sentence 'The proposed approach achieves a 91% top-two accuracy' should be qualified as the ground-truth-PSF upper bound; the approximate-PSF results range from 75.5% to 88.6% (Table E.1).
  2. [§4.3, §3.1] There are several typos: 'radial basis functio' should be 'radial basis function' (§4.3), 'coefficients' appears as 'coefficients' (§3.1), and the ligature 'WaveDi ff' appears at multiple page breaks.
  3. [Figure 8 caption] The caption states that the S1 relative error is 2.5%, while §6.3.1, Table 2, and Table E.1 use 2.4%; make the numbers consistent.
  4. [§6.1.1, Eq. (8)] Equation (8) defines CM_{ij} with 1[\hat y = i], but a confusion-matrix entry should count a true class i assigned to predicted class j; the surrounding text also mixes the notions of 'row' and 'predicted labels' and should be aligned with the formula.
  5. [§6.2, §6.3.2] The statement that the method surpasses pixel-only classifiers by 'around 10%' should specify the metric (top-two accuracy) and the PSF-quality range, since the S1 row in Table E.1 does not show a clear advantage over the baselines.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the pipeline is a standard supervised setup; the same-model simulation is a validity limitation, not a logical circle.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs by construction. The similarity features (Eq. 4) are functions of the observed star image and the approximate PSF model; they are not fitted to the stellar labels. The SVM classifier is trained on these features with known labels and evaluated on a held-out test set of 1,000 stars, so reported accuracies (e.g., 91% top-two with ground-truth PSF) are measured outcomes, not re-statements of the training data. The approximate PSF models are fitted to separate star observations, and the PSF-aware classifier uses them only as auxiliary inputs; no parameter is renamed as a prediction. The proof-of-concept PSF improvement loop (Sect. 6.3.3) uses SEDs inferred from an approximate PSF to refine that same PSF, but the relative error of the improved PSF is evaluated against ground-truth PSF samples on test stars, so the improvement is not guaranteed by the loop's construction. The citations to WaveDiff and the PSF-model notation (Liaudat et al. 2023a,b) are normal tool/notation citations with overlapping authors, but they are not load-bearing: the method is not mathematically derived from WaveDiff, and the paper states similar performance is expected from any chromatic PSF model. The use of the same simulator to generate both ground truth and approximate PSF models means the study does not test PSF model misspecification on real data, a limitation for external validity, but this is not a circularity of the paper's derivation. No step in the argument asserts that X is true because the paper's own prior work says so; the empirical claims rest on the simulations and metrics presented here.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The method's free parameters are modest but real: the bin count (8), SVM hyperparameters (not reported), and baseline model architectures. The key axioms are the point-source observation model (Eq. 2), the assumption that WaveDiff's WFE representation is the correct family for the true PSF (true by construction in the simulations), and the assumption that 8 wavelength bins and 13 Pickles templates are sufficient proxies for real stellar diversity. No new physical entities are introduced; the 'similarity features' are a constructed transform, not a postulate with independent evidence.

free parameters (3)
  • n_lambda: number of spectral bins / similarity features = 8
    Set to 8 to speed computation; used to approximate Eq. 1 by Eq. 2 and defines the dimension of similarity features. Section 5.3.
  • SVM hyperparameters (C, gamma for RBF kernel) = not reported (scikit-learn defaults assumed)
    No tuning procedure is given; decision boundaries depend on these values. Section 4.3.
  • PCA components and CNN architecture for baseline models = 24 PCA coefficients; 32 channels, 6 convolutional layers
    Chosen for the baseline models without reported optimization; affects baseline comparisons. Sections 3.1 and 3.2.
assumptions (6)
  • domain assumption An unresolved star observation is a SED-weighted sum of monochromatic PSFs plus additive Gaussian noise (Eq. 2)
    Underpins the entire simulation and the similarity feature definition in Sect. 4.2; ignores detector complexities such as correlated noise and non-Gaussian pixel response.
  • ad hoc to paper The WaveDiff WFE representation captures the true PSF without model misspecification
    The simulated ground-truth PSF is generated by the same WaveDiff code used for the approximate models, so the evaluation does not test model mismatch. Sections 5 and Appendix C.
  • ad hoc to paper Eight wavelength bins are sufficient to discriminate the 13 spectral types
    Stated in Sect. 5.3; the visual separation in Fig. 4 is offered as support, but no resolution study is carried out.
  • domain assumption Top-two accuracy is the relevant metric for PSF modelling use
    Adjacent spectral classes differ by less than photometric noise (Sect. 6.1.3); exact accuracy is only 54.9% with the ground-truth PSF.
  • domain assumption The star sample is free of contamination by galaxies, binaries, and other sources
    Stated in Sect. 3; real star selection will introduce confusion not modeled here.
  • domain assumption Pickles (1998) templates represent stellar SEDs in the Euclid VIS passband
    Used to simulate observations and labels; real stars have a variety of metallicity, gravity, and interstellar reddening effects.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Breaking the degeneracy in stellar spectral classification from single wide-band images." pith.science (2026). https://pith.science/paper/JPTIKLNV

@misc{pith2026250116151,
  author       = {Pith},
  title        = {Pith review of: Breaking the degeneracy in stellar spectral classification from single wide-band images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JPTIKLNV}},
  note         = {Machine review of arXiv:2501.16151}
}
read the original abstract

The spectral energy distribution (SED) of observed stars in wide-field images is crucial for chromatic point spread function (PSF) modelling methods, which use unresolved stars as integrated spectral samples of the PSF across the field of view. This is particularly important for weak gravitational lensing studies, where precise PSF modelling is essential to get accurate shear measurements. Previous research has demonstrated that the SED of stars can be inferred from low-resolution observations using machine-learning classification algorithms. However, a degeneracy exists between the PSF size, which can vary significantly across the field of view, and the spectral type of stars, leading to strong limitations of such methods. We propose a new SED classification method that incorporates stellar spectral information by using a preliminary PSF model, thereby breaking this degeneracy and enhancing the classification accuracy. Our method involves calculating a set of similarity features between an observed star and a preliminary PSF model at different wavelengths and applying a support vector machine to these similarity features to classify the observed star into a specific stellar class. The proposed approach achieves a 91\% top-two accuracy, surpassing machine-learning methods that do not consider the spectral variation of the PSF. Additionally, we examined the impact of PSF modelling errors on the spectral classification accuracy.

Figures

Figures reproduced from arXiv: 2501.16151 by the authors.

Figure 2
Figure 2. CNN+MLP model diagram. In light blue the convolutional blocks. In yellow the multi-layer perceptron classifier. 3.1. PCA MLP The method proposed by Kuntzer et al. (2016) can be separated into two steps: the preprocessing of the input data and the ac￾tual spectral classification. The first step aims to extract rele￾vant structure from the observations by compressing the input into a reduced number of coefficients. Th… view at source ↗
Figure 1
Figure 1. PCA decomposition of input stars. (a) First seven PCA compo￾nents and PCA mean. (b) Original star observation and its reconstruc￾tion from the first 24 PCA components. The last figure in the lower panel shows the relative values of the coefficients associated with the 24 PCA components. Equation 1 describes the observational model of an unre￾solved star. The PSF of a telescope at the position of the star in the FOV … view at source ↗
Figure 3
Figure 3. Ilustrative example of the degeneracy between the PSF size and spectral type of stars. (a) Middle rows: monochromatic PSFs for two positions in the FOV. The PSFs are shown for eight equally spaced wavelength values. Top and bottom: eight-bin spectral energy distribution of two stars, a M5 star (top) and an O5 star (bottom), located at positions 1 and 2 respectively. The wavelength axis is shared between all rows. (b… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Normalised similarity features as a function of monochromatic PSF wavelength for the 10 000 stars. Each set of features is coloured according to the corresponding observation stellar type. ( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 6
Figure 6. Figure 6: Spectral templates for the 13 stellar classes taken from Pickles (1998). Spectra are limited to a Euclid-like passband [550 − 900] nm, with a resolution of 1 nm. Spectra are flux normalised to unit sum. follows, SEDb k (λk) = 1 wb k Z λk+∆b k /2 λk−∆b k /2 fstar(λ)dλ, …
Figure 7
Figure 7. Figure 7: Project workflow: 13 000 star observations were simulated with the WaveDiff PSF simulator. Each star observation is located at a particular FOV position (ui , vi), has a random noise level S/N and belongs to a spectral class Ci . 10 000 stars are directly used for trai…
Figure 10
Figure 10. Figure 10: Accuracy (dashed blue line) and top-two accuracy (continuous blue line) metrics for the PSF-aware model (SVM+PSF) as a function of the PSF model error. In red and violet (horizontal lines), correspond￾ing metrics for the pixel-only classification methods (PCA+MLP and …
Figure 8
Figure 8. Figure 8: F1 score, accuracy, and top-two accuracy by stellar type for the PCA+MLP, CNN+MLP, and SVM+PSF models. The SVM+PSFS1 line shows the SVM+PSF classifier that uses the similarity features computed with an approximate PSF model trained on the S1 dataset, which has a relati…
Figure 9
Figure 9. Figure 9: Relative error at observation resolution for each approximate PSF model as a function of the number of training stars. The error bars represent the standard deviation of the relative errors of the stars in the test dataset [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 12
Figure 12. Figure 12: shows the relative error, at observation resolution, of the PSF model as a function of the number of training stars. In dark yellow, we present the baseline relative error of the approx￾imate PSF model (i.e. trained on the 50 stars with GT SEDs). The relative error of…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 32 canonical work pages

  1. [1]

    2019, The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s

    Akeson, R., Armus, L., Bachelet, E., et al. 2019, The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s

    work page 2019

  2. [2]

    2022, Frontiers in Astronomy and Space Sciences, 9

    Akhaury, U., Starck, J.-L., Jablonka, P., Courbin, F., & Michalewicz, K. 2022, Frontiers in Astronomy and Space Sciences, 9

    work page 2022

  3. [3]

    Baer, R. L. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 6068, Sensors, Cameras, and Systems for Scien- tific/Industrial Applications VII, ed. M. M. Blouke, 37–48

    work page 2006

  4. [4]

    2003, The Messenger, 114, 10

    Bagnulo, S., Jehin, E., Ledoux, C., et al. 2003, The Messenger, 114, 10

    2003

  5. [5]

    2012, in Proceedings of Machine Learning Research, V ol

    Baldi, P. 2012, in Proceedings of Machine Learning Research, V ol. 27, Pro- ceedings of ICML Workshop on Unsupervised and Transfer Learning, ed. I. Guyon, G. Dror, V . Lemaire, G. Taylor, & D. Silver (Bellevue, Washington, USA: PMLR), 37–49

    work page 2012

  6. [6]

    1996, A&AS, 119, 373

    Baranne, A., Queloz, D., Mayor, M., et al. 1996, A&AS, 119, 373

    1996

  7. [7]

    2004, in Scientific Detectors for Astron- omy, ed

    Basden, A., Tubbs, B., & Mackay, C. 2004, in Scientific Detectors for Astron- omy, ed. P. Amico, J. W. Beletic, & J. E. Beletic (Dordrecht: Springer Nether- lands), 599–602

    work page 2004

  8. [8]

    2011, in Astronomical Society of the Pacific Conference Series, V ol

    Bertin, E. 2011, in Astronomical Society of the Pacific Conference Series, V ol. 442, Astronomical Data Analysis Software and Systems XX, ed. I. N. Evans, A. Accomazzi, D. J. Mink, & A. H. Rots, 435

    2011

Show all 42 references
  1. [9]

    & Arnouts, S

    Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393

    1996

  2. [10]

    1995, Neural networks for pattern recognition (Oxford University

    Bishop, C. 1995, Neural networks for pattern recognition (Oxford University

    1995

  3. [11]

    2023, MNRAS, 518, 3123

    Chaini, S., Bagul, A., Deshpande, A., et al. 2023, MNRAS, 518, 3123

    2023

  4. [12]

    2013, Monthly Notices of the Royal Astronomical Society, 431, 3103 Euclid Collaboration, Cropper, M., Al-Bahlawan, A., et al

    Cropper, M., Hoekstra, H., Kitching, T., et al. 2013, Monthly Notices of the Royal Astronomical Society, 431, 3103 Euclid Collaboration, Cropper, M., Al-Bahlawan, A., et al. 2024a, Euclid. II. The VIS Instrument Euclid Collaboration, Mellier, Y ., Abdurro’uf, et al. 2024b, Euc...

    2013

  5. [13]

    Farrens, S., Lacan, A., Guinot, A., & Vitorelli, A. Z. 2022, A&A, 657, A98 Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1

    2022

  6. [14]

    R., Schrabback, T., Marggraf, O., et al

    Gillis, B. R., Schrabback, T., Marggraf, O., et al. 2020, Monthly Notices of the Royal Astronomical Society, 496, 5017

    2020

  7. [15]

    2020, Metrics for Multi-Class Classifica- tion: an Overview

    Grandini, M., Bagli, E., & Visani, G. 2020, Metrics for Multi-Class Classifica- tion: an Overview

    2020

  8. [16]

    W., Rhodes, J., Massey, R., & Ellis, R

    High, F. W., Rhodes, J., Massey, R., & Ellis, R. 2007, PASP, 119, 1295

    2007

  9. [17]

    M., Miller, C

    Hopkins, A. M., Miller, C. J., Connolly, A. J., et al. 2002, The Astronomical Journal, 123, 1086 Ivezi´c, Z., Kahn, S. M., Tyson, J. A., et al. 2019, The Astrophysical Journal, 873, 111

    2002

  10. [18]

    M., Amon, A., et al

    Jarvis, M., Bernstein, G. M., Amon, A., et al. 2020, Monthly Notices of the Royal Astronomical Society, 501, 1282

    2020

  11. [19]

    Kramer, M. A. 1991, AIChE Journal, 37, 233

    1991

  12. [20]

    Krizhevsky, A., Sutskever, I., & Hinton, G. E. 2012, in Advances in Neural Infor- mation Processing Systems, ed. F. Pereira, C. Burges, L. Bottou, & K. Wein- berger, V ol. 25 (Curran Associates, Inc.)

    2012

  13. [21]

    2016, A&A, 591, A54

    Kuntzer, T., Tewes, M., & Courbin, F. 2016, A&A, 591, A54

    2016

  14. [22]

    Lauer, T. R. 1999, PASP, 111, 1434

    1999

  15. [23]

    2011, arXiv e-prints, arXiv:1110.3193

    Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv e-prints, arXiv:1110.3193

    2011 arXiv

  16. [24]

    S., et al

    LeCun, Y ., Boser, B., Denker, J. S., et al. 1989, Neural Computation, 1, 541

    1989

  17. [25]

    2021, A&A, 646, A27 LSST Science Collaboration, Abell, P

    Liaudat, T., Bonnin, J., Starck, J.-L., et al. 2021, A&A, 646, A27 LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, LSST Science

    2021

  18. [26]

    2018, Annual Review of Astronomy and Astrophysics, 56, 393

    Mandelbaum, R. 2018, Annual Review of Astronomy and Astrophysics, 56, 393

    2018

  19. [27]

    2012, Monthly Notices of the Royal Astronomical Society, 429, 661

    Massey, R., Hoekstra, H., Kitching, T., et al. 2012, Monthly Notices of the Royal Astronomical Society, 429, 661

    2012

  20. [28]

    W., Keenan, P

    Morgan, W. W., Keenan, P. C., & Kellman, E. 1943, An atlas of stellar spectra, with an outline of spectral classification (The University of Chicago press) Ngolè, F., Starck, J.-L., Okumura, K., Amiaux, J., & Hudelot, P. 2016, Inverse Problems, 32, 124001

    1943

  21. [29]

    Noll, R. J. 1976, J. Opt. Soc. Am., 66, 207

    1976

  22. [30]

    Paulin-Henriksson, S., Amara, A., V oigt, L., Refregier, A., & Bridle, S. L. 2008, A&A, 484, 67

    2008

  23. [31]

    2018, Scikit-learn: Machine Learning in Python

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2018, Scikit-learn: Machine Learning in Python

    2018

  24. [32]

    Perryman, M. A. C., de Boer, K. S., Gilmore, G., et al. 2001, A&A, 369, 339

    2001

  25. [33]

    Pickles, A. J. 1998, Publications of the Astronomical Society of the Pacific, 110, 863 Sánchez-Blázquez, P., Peletier, R. F., Jiménez-Vicente, J., et al. 2006, MNRAS, 371, 703

    1998

  26. [34]

    J., Teuben, P

    Sault, R. J., Teuben, P. J., & Wright, M. C. H. 1995, in Astronomical Society of the Pacific Conference Series, V ol. 77, Astronomical Data Analysis Software and Systems IV , ed. R. A. Shaw, H. E. Payne, & J. J. E. Hayes, 433

    1995

  27. [35]

    Schaefer, C., Geiger, M., Kuntzer, T., & Kneib, J. P. 2018, A&A, 611, A2

    2018

  28. [36]

    H., Cañameras, R., et al

    Schuldt, S., Suyu, S. H., Cañameras, R., et al. 2021, A&A, 651, A55

    2021

  29. [37]

    2019, Monthly Notices of the Royal Astronomical Society, 491, 2280 Article number, page 11 of 15 A&A proofs: manuscript no

    Sharma, K., Kembhavi, A., Kembhavi, A., et al. 2019, Monthly Notices of the Royal Astronomical Society, 491, 2280 Article number, page 11 of 15 A&A proofs: manuscript no. aanda

    2019

  30. [38]

    2015, Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Re- port

    Spergel, D., Gehrels, N., Baltay, C., et al. 2015, Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Re- port

    2015

  31. [39]

    A., Singh, H

    Valdes, F., Gupta, R., Rose, J. A., Singh, H. P., & Bell, D. J. 2004, ApJS, 152, 251

    2004

  32. [40]

    Yang, Y . & Li, X. 2024, Universe, 10, 214

    2024

  33. [41]

    Zeiler, M. D. & Fergus, R. 2013, Visualizing and Understanding Convolutional Networks

    2013

  34. [42]

    2πi λ WFE(x, y|ui, vi) #)

    Zeiler, M. D., Taylor, G. W., & Fergus, R. 2011, in 2011 International Conference on Computer Vision, 2018–2025 Article number, page 12 of 15 E. Centofanti: PSF-aware spectral classification Appendix A: PSF modelling notation Table A.1. Coordinates and notation used throughout...

    2023

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.