Pith. sign in

REVIEW 2 major objections 4 minor 26 references

A Quasi-Optimal Stacking Method for Up-the-Ramp Readout Images

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read For non-destructive readout images, weighting frames by the inverse noise covariance with a target of SNR=1 per pixel outperforms equal-weight stacking and ramp fitting, and for CSST NIR data it would add about 0.5 magnitude of depth.

desk verdict A practical, well-derived stacking recipe for faint-source detection in up-the-ramp readouts, with a solid robustness study and a CSST estimate that needs a caveat about correlated readout noise before its headline numbers are used. read the letter →

arxiv 2501.08732 v1 pith:EPPTK2BD submitted 2025-01-15 astro-ph.IM

Guanghuan Wang , Hu Zhan , Zun Luo , Chengqi Liu , Youhua Xu , Chun Lin , Yanfeng Wei , WenLong Fan This is my paper · ORCID
classification astro-ph.IM
keywords up-the-rampreadoutnon-destructiveimagestackingsignal-to-noiseratiorampfittinginfrareddetectorsChinaSpaceStationTelescopeastronomicaldatareduction
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

The paper proposes a way to combine up-the-ramp detector frames—successive non-destructive reads of the same pixels during one exposure—into a single image that is nearly optimal for finding faint objects. Because noise in these frames is correlated, the best linear combination uses unequal weights, and the paper derives the weights that maximize signal-to-noise ratio for a chosen target brightness. The authors then argue that targeting the faintest useful case, one signal-to-noise ratio unit per pixel in the last frame, is a safe choice: bright objects lose little, faint objects gain the most. They claim this quasi-optimal stacking always beats equal-weight stacking and ramp fitting in their simulated flat-field and point-source tests. For a 150-second CSST near-infrared exposure, stacking 30 frames would deepen the limiting magnitude by about 0.5 mag and cut effective readout noise by about 62%.

What carries the argument

The load-bearing object is the covariance matrix $C_{ij}=s_{\min(i,j)}+b_{\min(i,j)}+r^2\delta_{ij}$, which encodes the fact that Poisson fluctuations persist once accumulated, while readout noise appears only on the diagonal. Maximizing $\mathrm{SNR}=\mathbf{w}^T\mathbf{s}/\sqrt{\mathbf{w}^T C\mathbf{w}}$ gives the optimal weight vector $\mathbf{w}_{\mathrm{opt}}\propto C^{-1}\mathbf{s}$; the paper's method fixes the target SNR per pixel in the last frame to unity, computes these weights once, and applies the same weights to every pixel in a frame to preserve calibratability. The key insight is an asymmetry: using brighter-than-truth target weights hurts faint objects, while using fainter-than-truth target weights barely hurts bright objects, so targeting the faintest recoverable case is quasi-optimal.

What would settle it

Take a real near-infrared detector ramp sequence with a known flat background and measure the covariance matrix $C_{ij}$ from many pixels. If the off-diagonal entries deviate from $\min(s_i+b_i,s_j+b_j)$ beyond the readout noise, or if the diagonal variances are not equal across frames, the derived weights are no longer optimal; a direct test would compare the SNR of real ramp stacks reduced with the paper's weights against the last-frame and equal-weight methods and check the predicted gain of roughly 60% in SNR.

Watch

Extended reading notes

Core claim

The central discovery is that a single global set of stacking weights, derived from the noise covariance under the target assumption $\mathrm{SNR_{last}}=1$, achieves signal-to-noise ratio per pixel at or near the theoretical optimum across a wide range of source brightness, whereas weights tuned to brighter targets degrade faint sources severely. The paper expresses the optimal weights as $\mathbf{w}_{\mathrm{opt}}\propto C^{-1}\mathbf{s}$, where $C$ is the covariance of pixel values across frames and $\mathbf{s}$ is the signal vector, and shows numerically and with simulations that the SNR loss is under 1% for $\mathrm{SNR_{last}}$ up to 10 when targeting $\mathrm{SNR_{target}}=1$. In flat-field and point-source simulations spanning readout-, background-, and photon-noise dominated regimes, the method outperforms equal-weight stacking, ramp fitting, and the last-frame benchmark, except that at very high SNR in the photon-noise dominated regime the last frame eventually wins. For the CSST NIR imager, the method converts 30 up-the-ramp frames into roughly 0.5 mag of additional limiting depth.

Load-bearing premise

The whole derivation rests on the assumption that each pixel's noise is exactly the sum of two independent Poisson processes (source and background) plus Gaussian readout noise with the same variance in every frame and no correlation between frames; real detectors often have correlated readout noise, 1/f noise, persistence, or cosmic-ray jumps that would make the derived weights suboptimal and could shrink the claimed gains.

Editorial extensions

If this is right

  • For any up-the-ramp data set with the assumed noise covariance, choosing $\mathrm{SNR_{target}}=1$ yields stacked SNR within a few percent of the per-pixel optimum up to high $\mathrm{SNR_{last}}$, so one weight set serves an entire survey.
  • In readout-noise-dominated observations, the method recovers most of the SNR that destructive-readout observers lose, improving faint-source detection without extra exposure time.
  • The method avoids the instability of ramp fitting when only a few up-the-ramp exposures are available.
  • For CSST NIR with 30 frames, limiting magnitude improves by about 0.5 mag and effective readout noise falls by about 62%, with modest additional gain to about 0.6 mag and 71% at 70 frames.
  • At very high SNR in the photon-noise dominated regime the last-frame method can surpass it, so the gain is concentrated exactly at the detection threshold where it matters.

Reading between the lines

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

  • The derivation is independent of the telescope, so the same weights should transfer to other non-destructive-readout cameras, provided the noise is dominated by uncorrelated Poisson and readout terms.
  • If correlated readout noise or 1/f noise is measured, the covariance matrix $C$ could be augmented with off-diagonal terms beyond the diagonal readout term, and the same $C^{-1}\mathbf{s}$ recipe would produce weights for those detectors.
  • A practical extension for cosmic-ray rejection would be to flag and clean jumps before weighting, since the weights assume no jumps; the paper does not model this.
  • The CSST 0.5 mag estimate assumes a perfectly Poisson background and Gaussian readout, so it would need end-to-end verification on real detector calibration data before being used in an observing plan.
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

2 major / 4 minor

Summary. This paper proposes a weighted stacking method for up-the-ramp (non-destructive readout) images. The authors derive the optimal weights ω ∝ C^{-1}s for a pixel whose covariance C follows from Poisson signal/background fluctuations plus frame-independent Gaussian readout noise (Eqs. (2)-(6)). Because a single weight set must serve all pixels of different brightness, they select the weights that maximize SNR for a target case of SNR=1 in the last frame, calling the result quasi-optimal. They compare this method with equal-weight stacking, ramp fitting, and simply taking the last frame, using simulated flat-field images and point-source images (Section 3). The paper reports that the quasi-optimal method yields the highest SNR in the tested regimes (with the last frame eventually winning in the high-SNR photon-noise-dominated regime), and it estimates that for CSST NIR observations, stacking 30 up-the-ramp frames improves the limiting magnitude by about 0.5 mag and reduces effective readout noise by about 62% (Section 4, Table 4).

Significance. The analytic derivation in Section 2 is clean and correct under the stated covariance model, and the method has practical appeal: a single set of frame-wise weights preserves easy flux calibration, and the SNR_target=1 choice is well motivated for faint extended or point sources. The simulations are clearly described and support the relative ranking of the methods within the tested parameter space. The CSST forecast, if validated against realistic detector noise, is actionable for the instrument's observing strategy. However, the quantitative claims—both the 'always better' simulation result and the 0.5 mag/62% CSST improvement—rest entirely on an idealized noise model with uncorrelated readout noise and pure Poisson fluctuations, and the paper itself cites but does not incorporate the known correlated-readout-noise behavior of near-IR arrays. The practical significance is therefore real but not yet fully established.

major comments (2)
  1. [Section 2, Eq. (2); Section 4, Table 4] The covariance model C_ij = s_min(i,j) + b_min(i,j) + r^2 δ_ij assumes pure Poisson signal/background and readout noise that is independent across frames with identical variance. This is the single load-bearing assumption behind the claim that the quasi-optimal method outperforms equal-weight and ramp fitting, and behind the CSST limiting-magnitude and effective-readout-noise numbers. Real HgCdTe NIR arrays, including those planned for CSST, exhibit correlated readout noise (1/f, common-mode, row/column correlations), and the paper cites the Euclid NISP study of this effect (Ref [6]) without letting it enter the simulations or the CSST estimate. As a result, the reader cannot tell whether the 0.5 mag and 62% improvements survive realistic detector behavior. I request either additional simulations with a correlated-readout-noise component (for example, a simple 1/f or common-mode model) or a quantitative literature-based argument bounding the degradation; alternatively, the paper should explicitly frame the conclusions as conditional on the white-readout-noise model.
  2. [Section 3.1] The sentence defining the flat-field SNR reads: 'The SNR is given by the ratio of the standard deviation of all pixels in the reduced image to the mean of these pixels.' This is the inverse of the SNR definition in Eq. (2) and of the values actually plotted in Figure 3 (which must be mean/std to reach SNR_last≈1 for the Table 2 parameters). Please correct this typo and write the formula explicitly so that the simulation metric is unambiguous.
minor comments (4)
  1. [Abstract and Section 5] The abstract says the quasi-optimal method 'always enhances the SNR more than the equal-weight stacking method and the ramp fitting method.' Although this is not formally contradicted by the conclusion (which concedes that the last-frame method wins at high SNR in the photon-noise-dominated regime), the word 'always' is stronger than what the finite, idealized simulations support. Please qualify it as 'in the simulated regimes under the stated noise model' to match the scope of the evidence.
  2. [Section 4, Eq. (13)] The symbol b in Eq. (13) is used without definition; from context it is the background count per pixel accumulated by the last frame, but this should be stated explicitly to make the effective-readout-noise formula reproducible.
  3. [Section 4, Table 4] The limiting magnitudes and effective readout noise values in Table 4 are quoted to two decimals with no uncertainties or sensitivity analysis. Given the assumed system throughput, sky background, and readout noise are all stated with inequalities or handbook values, a simple parameter variation (e.g., ±10% in throughput and sky background) would help the reader assess the robustness of the 0.5 mag and 62% headlines.
  4. [General] Section 3.2 reports point-source SNR boosts of '57–70%' for four specific input flux levels, but the figure labels also list the resulting aperture SNRs. Adding the noise realizations or the number of trials used for those aperture photometry measurements would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optimal-weight derivation is a self-contained mathematical result, the simulations are forward draws from an explicit noise model, and the CSST estimates are parameterized predictions; self-citations are contextual only.

full rationale

The paper's central chain is not circular. The optimal weights are derived by maximizing the SNR expression in Eq. (2), giving w ∝ C^{-1}s in Eq. (5) under an explicitly stated covariance model C_ij = s_min(i,j) + b_min(i,j) + r^2 delta_ij. This is a direct application of the Cauchy-Schwarz / Rayleigh-quotient argument, not a quantity fitted to the data that is later relabeled as a prediction. The choice SNR_target = 1 is a stated design decision, not a fitted parameter. The simulated flat-field and point-source images are generated from the same covariance model, but the comparison is a forward demonstration of the already-derived optimality, and the robustness to target mismatch (Fig. 2) is a nontrivial numerical result. The CSST limiting-magnitude and effective-readout-noise estimates are forward calculations from telescope parameters, the star-count formula in Eq. (11), and photometric SNRs measured on independent simulations; the effective readout noise in Eq. (13) is a definition that restates the SNR gain, but it is not used as an input to produce that gain. The self-citations (Refs. [9] and [10], by author Zhan) provide mission context for CSST and do not carry the derivation; the ramp-fitting noise formulas cited as Ref. [23] come from a different author. The skeptical concern about correlated readout noise, 1/f noise, or persistence is a realism/validity limitation of the assumed noise model, not a circularity: the internal mathematics is self-consistent and the claims are explicitly conditional on that model. No quoted passage exhibits a step where a defined quantity is used to predict itself or where a fitted value is renamed as an independent result.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

Free parameters: SNR_target=1 chosen by hand; no constants fitted to data. Axioms: uncorrelated constant-variance readout noise; linear signal and background with equally spaced frames; per-frame uniform weights as a calibration-motivated design choice. No invented entities.

free parameters (1)
  • SNR_target = 1
    Hand-chosen target SNR per pixel in the last frame used to derive the stacking weights; chosen based on robustness simulations in Section 2, not fitted to external data.
assumptions (3)
  • domain assumption Readout noise is Gaussian, independent between frames, and has the same variance r^2 in every frame.
    The covariance matrix in Section 2 (Eqs. 1-2) assumes this; real detectors, e.g., Euclid NISP (ref [6]), exhibit correlated readout noise.
  • domain assumption Frames are evenly spaced in time and signal and background increase exactly linearly with time after bias and non-linearity correction.
    Stated after Eq. (7): 'we assume hereafter for convenience that the frames are equally spaced in time'; the SNR optimization uses this linear ramp model.
  • domain assumption The same weight vector is applied to all pixels in a frame, giving one scalar weight per frame.
    Design choice in Section 2 to preserve calibration; it makes the stack suboptimal per pixel but is not a physical assumption.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Quasi-Optimal Stacking Method for Up-the-Ramp Readout Images." pith.science (2026). https://pith.science/paper/EPPTK2BD

@misc{pith2026250108732,
  author       = {Pith},
  title        = {Pith review of: A Quasi-Optimal Stacking Method for Up-the-Ramp Readout Images},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPPTK2BD}},
  note         = {Machine review of arXiv:2501.08732}
}
read the original abstract

The non-destructive readout mode of a detector allows its pixels to be read multiple times during integration, generating a series of "up-the-ramp" images that keep accumulating photons between successive frames. Since the noise is correlated across these images, an optimal stacking generally requires weighting them unequally to achieve the best signal-to-noise ratio (SNR) for the target. Objects in the sky show wildly different brightness, and the counts in the pixels of the same object also span a wide range. Therefore, a single set of weights cannot be optimal for all cases. To keep the stacked image more easily calibratable, however, we choose to apply the same weight to all the pixels in the same frame. In practice, we find that the results of high-SNR cases degrade only slightly by adopting weights derived for low-SNR cases, whereas the low-SNR cases are more sensitive to the weights applied. We therefore propose a quasi-optimal stacking method that maximizes the stacked SNR for the case of SNR=1 per pixel in the last frame and demonstrate with simulated data that it always enhances the SNR more than the equal-weight stacking method and the ramp fitting method. Furthermore, we give an estimate of the improvement of limiting magnitudes for the China Space Station Telescope (CSST) based on this method. Compared with the conventional readout mode, which is equivalent to taking the last frame of the non-destructive readout, stacking 30 up-the-ramp images can improve the limiting magnitude by about 0.5 mag for CSST near-infrared observations, effectively reducing the readout noise by about 62%.

Figures

Figures reproduced from arXiv: 2501.08732 by the authors.

Figure 1
Figure 1. Optimal stacking weights. Lines of differ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. SNR degradation of stacking with non-optimal [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. SNR per pixel of reduced flat-field images with the quasi-optimal stacking method (red solid curve for SNR [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Mock stellar images reduced from the ramp series using different methods. From left to right, the panels in each [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

  1. [6]

    J., Mac´ ıas-P´ erez, J., Secroun, A., et al

    Mu˜ noz, A. J., Mac´ ıas-P´ erez, J., Secroun, A., et al. 2021, Euclid: Estimation of the impact of correlated readout noise for flux measurements with the Euclid NISP instrument, Publications of the Astronomical Society of the Pacific, 133 (1027), 094502

    work page 2021

  2. [1]

    J., Bergeron, L

    Skinner, C. J., Bergeron, L. E., Schultz, A. B., et al. 1998, in Infrared Astronomical Instrumentation, Vol. 3354, SPIE, 2–13

    work page 1998

  3. [2]

    2008, in High Energy, Optical, and Infrared Detectors for Astronomy III, Vol

    Baggett, S., Hill, R., Kimble, R., et al. 2008, in High Energy, Optical, and Infrared Detectors for Astronomy III, Vol. 7021, SPIE, 527–537

    work page 2008

  4. [3]

    G., Hora, J

    Fazio, G. G., Hora, J. L., Willner, S. P., et al. 1998, in Infrared Astronomical Instrumentation, Vol. 3354, SPIE, 1024–1031

    work page 1998

  5. [4]

    2007, Infrared detector arrays for astronomy, Annu

    Rieke, G. 2007, Infrared detector arrays for astronomy, Annu. Rev. Astron. Astrophys., 45, 77–115

    work page 2007

  6. [5]

    2012, in Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, Vol

    Corcione, L., Ligori, S., Bortoletto, F., et al. 2012, in Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, Vol. 8442, SPIE, 1101–1112

    work page 2012

  7. [7]

    Casertano, S. 2022, Determining the Best-Fitting Slope and its Uncertainty for Up-the-Ramp Sampled Images with Unevenly Distributed Resultants, Nancy Grace Roman Space Telescope (Roman) Technical Report Roman-STScI-000394,

    work page 2022

  8. [8]

    J., Arendt, R

    Rauscher, B. J., Arendt, R. G., Fixsen, D. J., et al. 2019, Principal component analysis of up-the-ramp sampled infrared array data, Journal of Astronomical Telescopes, Instruments, and Systems, 5 (2), 028001– 028001

    work page 2019

Show all 26 references
  1. [9]

    Zhan, H. 2011, Consideration for a large-scale multi- color imaging and slitless spectroscopy survey on the Chinese space station and its application in dark energy research, Scientia Sinica Physica, Mechanica & Astronomica, 41(12), 1441

    2011

  2. [10]

    Zhan, H. 2021, The wide-field multiband imaging and slitless spectroscopy survey to be carried out by the Survey Space Telescope of China Manned Space Program, Chinese Science Bulletin, 66(11), 1290– 1298

    2021

  3. [11]

    2019, Cosmology from the Chinese Space Station Optical Survey (CSS- OS), The Astrophysical Journal, 883(2), 203

    Gong, Y., Liu, X., Cao, Y., et al. 2019, Cosmology from the Chinese Space Station Optical Survey (CSS- OS), The Astrophysical Journal, 883(2), 203

    2019

  4. [12]

    2024, Research of IRFPA ROIC for astronomy, Infrared and Laser Engineering, 53 (1), 20230364–1

    Qinghua, L., Yanfeng, W., Honglei, C., Jing, G., & Ruijun, D. 2024, Research of IRFPA ROIC for astronomy, Infrared and Laser Engineering, 53 (1), 20230364–1

    2024

  5. [13]

    W., Croll, B., & Simcoe, R

    Sullivan, P. W., Croll, B., & Simcoe, R. A. 2014, in High Energy, Optical, and Infrared Detectors for Astronomy VI, Vol. 9154, SPIE, 467–475

    2014

  6. [14]

    E., & Gordon, K

    Anderson, R. E., & Gordon, K. D. 2011, Optimal cosmic-ray detection for nondestructive read ramps, Publications of the Astronomical Society of the Pacific, 123(908), 1237

    2011

  7. [15]

    2001, Validation of Up-the-Ramp Sampling with Cosmic- Ray Rejection on Infrared Detectors, Publications of the Astronomical Society of the Pacific, 113(780), 240

    Offenberg, J., Fixsen, D., Rauscher, B., et al. 2001, Validation of Up-the-Ramp Sampling with Cosmic- Ray Rejection on Infrared Detectors, Publications of the Astronomical Society of the Pacific, 113(780), 240

    2001

  8. [16]

    2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Robberto, M. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9143, Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ed. J. Oschmann, Jacobus M., M. Clampin, G. G. Fazio, & H. A. MacEwen, 91433Z

    2014

  9. [17]

    2000, Cosmic-Ray Rejection and Readout Efficiency for Large-Area Arrays, Publications of the Astronomical Society of the Pacific, 112 (776), 1350

    Fixsen, D., Offenberg, J., Hanisch, R., et al. 2000, Cosmic-Ray Rejection and Readout Efficiency for Large-Area Arrays, Publications of the Astronomical Society of the Pacific, 112 (776), 1350

    2000

  10. [18]

    2017, in Proceedings of the 11th International Conference on distributed smart cameras, 21–28

    Darson, D., Dubois, J., Bourdernane, M., et al. 2017, in Proceedings of the 11th International Conference on distributed smart cameras, 21–28

    2017

  11. [19]

    2010, Research of NDR to Enhance the Dynamic Range of CMOS Image Sensor, Microcomputer Information, 26(10), 7–9

    Junhua, P. 2010, Research of NDR to Enhance the Dynamic Range of CMOS Image Sensor, Microcomputer Information, 26(10), 7–9

    2010

  12. [20]

    2023, in WFC3 Instrument Handbook for Cycle 31 v

    Dressel, L., & Marinelli, M. 2023, in WFC3 Instrument Handbook for Cycle 31 v. 15.0, Vol. 15, 97–98, 286–290

    2023

  13. [21]

    D., Rieke, G

    Gordon, K. D., Rieke, G. H., Engelbracht, C. W., et al. 2005, Reduction algorithms for the multiband imaging photometer for spitzer, Publications of the Astronomical Society of the Pacific, 117 (831), 503

    2005

  14. [22]

    D., & Forrest, W

    Garnett, J. D., & Forrest, W. J. 1993, in Infrared Detectors and Instrumentation, Vol. 1946, SPIE, 395–404

    1993

  15. [23]

    2007, Analysis of the sampling schemes for WFC3-IR, WFC3 ISR, 12

    Robberto, M. 2007, Analysis of the sampling schemes for WFC3-IR, WFC3 ISR, 12

    2007

  16. [24]

    J., Fox, O., Ferruit, P., et al

    Rauscher, B. J., Fox, O., Ferruit, P., et al. 2007, Detectors for the James Webb Space Telescope Near-Infrared Spectrograph. I. Readout Mode, Noise Model, and Calibration Considerations, Publications of the Astronomical Society of the Pacific, 119 (857), 768

    2007

  17. [25]

    2016, SEP: Source Extractor as a library, Journal of Open Source Software, 1 (6), 58

    Barbary, K. 2016, SEP: Source Extractor as a library, Journal of Open Source Software, 1 (6), 58

    2016

  18. [26]

    1996, SExtractor: Software for source extraction, Astronomy and astrophysics 10 ASTRONOMICAL TECHNIQUES & INSTRUMENTS supplement series, 117 (2), 393–404

    Bertin, E., & Arnouts, S. 1996, SExtractor: Software for source extraction, Astronomy and astrophysics 10 ASTRONOMICAL TECHNIQUES & INSTRUMENTS supplement series, 117 (2), 393–404

    1996

Pith tools

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