Learning neural representations for X-ray ptychography reconstruction with unknown probes

Hanfei Yan; Jizhou Li; Tingyou Li; Xiaojing Huang; Zirui Gao; Zixin Xu

REVIEW 4 major objections 4 minor 51 references

Learning neural representations for X-ray ptychography reconstruction with unknown probes

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read PtyINR claims that X-ray ptychography can jointly recover both the sample and the unknown illuminating probe from raw diffraction patterns by parameterizing each as a continuous neural field, and that this beats established solvers especial

desk verdict PtyINR: a credible blind probe+object INR for ptychography, but the 'consistent SOTA' claim needs repeated-seed stats and hyperparameter values. read the letter →

arxiv 2509.04402 v1 pith:IBZRUAME submitted 2025-09-04 cs.CV

Tingyou Li , Zixin Xu , Zirui Gao , Hanfei Yan , Xiaojing Huang , Jizhou Li This is my paper · ORCID

classification cs.CV

keywords X-rayptychographyimplicitneuralrepresentationblindreconstructionunknownproberecoveryself-supervisedlearninglow-doseimagingphaseretrievalcoherentdiffractive

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

X-ray ptychography records only the intensity of diffracted X-rays while the illuminating beam (the probe) is usually unknown, making image recovery a blind phase-retrieval problem. This paper proposes PtyINR, a self-supervised method that represents both the sample and the probe as continuous functions learned by neural networks, and trains them end-to-end by simulating diffraction patterns and comparing them with measurements. The central claim is that one unified network can recover both fields without probe pre-characterization or labeled training data, and that it does so more accurately than established iterative solvers (ePIE, DM, WASP, APG) and learning-based baselines, especially when overlap is low or the signal is noisy. If correct, this removes a major practical bottleneck: probes no longer need to be measured separately, and low-dose or radiation-sensitive samples become more accessible to high-resolution ptychography.

What carries the argument

The load-bearing object is the pair of implicit neural representations: a SIREN (sine-activated MLP) for the object and a multi-resolution hash-encoding network (Instant-NGP style) for the probe. The asymmetry matters because the probe contributes to every diffraction pattern, so its representation must train stably, while the object contributes only locally and needs expressive high-frequency modeling. The other key piece is the hybrid loss: a SmoothL1 interpolation between l1 and l2 in intensity space, plus a probe mean-amplitude regularization applied only in early training and a normalization constraint. Together these carry the blind joint recovery; the paper's ablations attribute the s

What would settle it

Simulate ptychographic data from a known two-mode probe, or impose known scan-position jitter, then run PtyINR and check whether the object error grows with the mode-mixture or position-error magnitude. A clean control is to give a conventional solver the true probe modes and exact positions under the same noise and see whether it recovers the object with higher fidelity than PtyINR; if so, the single-mode/exact-position assumption is the crucial limit of the central claim.

Watch

Extended reading notes

Core claim

PtyINR's discovery is that ptychographic blind reconstruction can be formulated as pure self-supervised neural-field fitting. The object is parameterized as two coordinate-to-value MLPs with periodic activations, giving amplitude and phase; the probe is parameterized by a multi-resolution hash-encoded ReLU network. The forward model computes the predicted far-field diffraction intensity by Fourier transform of the exit wave, and the networks are trained by minimizing a SmoothL1 loss between predicted and measured intensities. To make joint recovery stable, the probe amplitude is normalized and a mean-amplitude regularization is applied in early training. On simulated data with 40%, -540%, an

Load-bearing premise

The reconstruction assumes a single coherent probe mode and exactly known scan positions; if the real probe is partially coherent (multi-mode) or the scan positions drift, the recovered object and probe may absorb those mismatches and the claimed fidelity is not guaranteed.

Editorial extensions

If this is right

Separate probe characterization becomes unnecessary for high-quality ptychography; the probe is recovered from the same data as the object.
Sparse overlap and very short exposures become usable, extending ptychography to dose-sensitive and dynamic samples.
The two-network physics-loss recipe can be carried to other probe-dependent imaging geometries such as near-field and Bragg ptychography by replacing the forward model.
Because the object is a continuous function rather than a pixel grid, irregular scan geometries can be handled without grid-interpolation artifacts.
With abundant clean data the method is comparable to established solvers; its reported advantage concentrates in degraded, low-overlap, and low-dose regimes.

Reading between the lines

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

A testable generalization is that the stable-probe/expressive-object split of representations may be a general recipe for blind inverse problems: parameterize the globally shared unknown with a low-variance hash-encoded network and the target with a high-frequency sine network.
The early-training probe regularization suggests a curriculum strategy where the probe is constrained until the object forms a rough structure and then released; the same trick could be exported to other self-supervised joint estimation tasks.
Because the probe neural field is a continuous function of coordinates, a probe network trained on one beamline configuration might be transferred to new samples measured with the same optics, making reconstructions faster and more stable than starting from random probe initialization.
The single-mode assumption is the natural place to test limits: if the method is extended to multi-mode probes by adding a mode dimension to the probe network, one can check whether the regularization still prevents degenerate solutions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this paper is a credible INR-based blind ptychography method with the strongest claims in the low-overlap/noisy regimes, but the empirical evidence for 'consistently outperforms' isn't as solid as the prose makes it sound.

What is new: prior INR work in Fourier ptychography, adaptive optics, and tomography either assumed a known probe or didn't treat ptychographic blind recovery. PtyINR parameterizes the object with a SIREN and the probe with a hash-encoding ReLU network, and uses a SmoothL1 physics loss plus a probe-amplitude regularization during early training. When the probe is unknown, that's a real step forward. The simulation suite is extensive — overlap ratios down to -800%, three noise models, real data from FZP and MLL setups, exposure times down to 0.003s. The ablations in the supplement (loss function, omega0, regularization) suggest the authors looked at their failure modes and engineered around them. Code is reportedly released. That's a solid methods package.

The soft spots are about evidence for the headline claim. All PSNR numbers are single-run point estimates; the supplement admits that with both object and probe unknown, 'the reconstruction may fail entirely with a non-negligible probability.' That admission is honest, but it cuts directly against the word 'consistently.' No success rates, no error bars, no seed variations. The hyperparameters are tuned per scenario: omega0 varies with step size, beta ranges over three orders of magnitude, and the regularization strength lambda and cutoff k in Eq. 2 are never given values. The LiCoO2 amplitude channel is excluded post-hoc as 'non-informative' — a red flag unless explained. And the single-mode probe/known-position assumptions limit the real-data conclusions; the authors acknowledge that in the conclusion. The FRC analysis covers only object phase. These are not fatal, but they are exactly the places where a 'state-of-the-art' claim needs support.

Who it's for: researchers in X-ray ptychography/computational microscopy who want to see whether blind INR-based reconstruction is viable, especially for low-dose experiments. A referee should engage with it — the architecture design and the experimental breadth deserve serious evaluation. The authors should be pushed to provide repeated-seed statistics, actual hyperparameter values, and a clear account of the amplitude-channel exclusion before the claim should be accepted.

Recommendation: send it to peer review rather than desk-rejecting.

Referee Report

4 major / 4 minor

Summary. The paper proposes PtyINR, a self-supervised implicit neural representation framework for joint recovery of the object and the unknown illumination probe in X-ray ptychography. The object is parameterized by a SIREN and the probe by a multi-resolution hash-encoded ReLU MLP; training minimizes a SmoothL1 diffraction-consistency loss with a probe-amplitude regularization term. The authors report simulations over scanning overlap ratios, noise conditions, and real datasets (LiCoO2 and Siemens star, FZP and MLL optics) and claim consistent state-of-the-art performance, especially in sparse and low-signal regimes.

Significance. If the empirical claims are substantiated, this is a useful advance: it removes probe pre-characterization and paired training data, is applicable to standard ptychographic forward models, and could benefit low-dose experiments. The paper ships released code, includes extensive ablation studies in the supplementary material, and evaluates on real data from two focusing systems. However, the headline 'consistently outperforms' claim is currently supported only by single-run point estimates, and key controls are unreported, so the significance is conditional.

major comments (4)

[Results, Figs. 2–5; Supplementary Note, Fig. S15 (p. 24)] The central claim is that PtyINR 'consistently outperform[s] existing techniques' and shows 'remarkable robustness' in low-overlap/low-dose regimes. The evidence consists of single-run PSNR values. The supplement itself states that when object and probe are jointly unknown, 'the reconstruction may fail entirely with a non-negligible probability' (p. 24). No success rates, repeated-seed error bars, medians, or failure statistics are reported for the final architecture or for the baselines. Because random initialization and Adam make the method stochastic, a point estimate cannot support a consistency/robustness claim. Please report seed/initialization statistics (e.g., at least 10 runs) and success probabilities, particularly at -800% overlap and 0.003 s exposure.
[Methods, Eq. (2); Supplementary Note, Fig. S17] Several per-scenario controls are tuned but not quantified. Eq. (2) defines the regularization coefficient λ and cutoff k, but no numerical values are given anywhere in the paper. The Methods section only reports ranges (β between 1e-4 and 1e-1, learning rate 1e-5 to 1e-4), and Fig. S17 shows ω0 varied among 30, 90, and 300 without stating which value is used for each experiment in Figs. 2–5. Without a table of per-experiment hyperparameters, the reported gains may reflect per-scenario tuning rather than the method itself. Code release helps but does not replace reporting in the manuscript.
[Methods, Eq. (11); Results, Fig. 5e] The FRC-based resolution claim requires two independent reconstructions F1 and F2, but the paper never states how these were obtained (e.g., splitting scan positions, different random seeds, or separate measurement sets). If the two inputs are not truly independent, the half-bit threshold overestimates resolution. The protocol must be specified or replaced with a controlled metric.
[Conclusion; Abstract] The paper acknowledges single-mode probe and exact position assumptions in the Conclusion, but the Abstract describes the method as 'generalizable' and applicable to 'a wide range of computational microscopy problems.' In practice, partial coherence or scan-position errors can be absorbed into the reconstructed object and probe fields, which would undermine the claim of recovering the true probe under low-signal conditions. Please either scope the claims to the tested assumptions or include a mismatched-model experiment (e.g., a two-mode probe or position error).

minor comments (4)

[Results, Fig. 2] The negative overlap labels (-540%, -800%) are unintuitive; the text explains the actual overlap (95%, 50%, 30%) but the figure axes should carry a clarifying note.
[Results, Fig. 4] The LiCoO2 amplitude images are excluded as 'non-informative.' If this is due to weak absorption, that is plausible, but the criterion should be stated and the images shown in the supplement so readers can assess the choice.
[Supplementary Note, Fig. S15] The panel label '(Appropriate loss should be 0)' is unclear: it appears to refer to the regularization loss, but the text is ambiguous. Please rephrase and specify which loss should be zero.
[Introduction and Results] A few grammatical issues: 'we evaluates,' 'these methods fails,' and 'it fail to preserve' should be corrected. Also, the claim 'state-of-the-art' should be qualified because recent methods such as the stochastic ADMM of Ref. [22] are cited but not benchmarked.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: PtyINR is an empirical, self-supervised forward-model fit evaluated against external baselines; no input is renamed as a prediction.

full rationale

The paper's central claim is an empirical reconstruction-quality comparison. PtyINR parameterizes the object and probe as neural fields and minimizes a physics-based loss (Eq. 2) between measured and predicted diffraction patterns. The reconstruction target is not defined in terms of the evaluation metric, and the evaluation metric (PSNR against independent simulated/experimental references) is not folded into the training objective. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is smuggled in through self-citation. The author-overlapping references (e.g., [19] APG, [29] PtychoNet, [35] AD, [44] fly-scan ptychography) are used as baselines, background, or a standard acquisition model; none supplies the claimed superiority or forbids alternatives. The Supplementary Note's admission that blind reconstruction can fail with non-negligible probability (Fig. S15 and surrounding text) is a robustness limitation, not circularity. The absence of repeated-seed statistics and unreported hyperparameters (λ, k, β, ω0) is a statistical reporting concern that does not constitute a circular derivation. No specific equation or claim reduces to its own input by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method is an empirical inverse-problem solver, not a derivation. The ledger captures the modeling choices and tuned knobs that the reconstructions depend on: the forward Fourier model, the single-mode and exact-position assumptions, the MLP representation choices, and the per-experiment hyperparameters (omega_0, beta, lambda/k, learning rate).

free parameters (4)

omega_0 (first-layer sine frequency in object SIREN) = 30, 90, or 300 depending on data regime
Supplementary Note and Fig. S17: higher values capture fine detail with dense clean data; lower values are needed for sparse or noisy data. This is a per-task choice.
beta (SmoothL1 threshold) = between 1e-4 and 1e-1 depending on the task
Methods section: 'the weighting coefficient beta ... varied between 10^-4 and 10^-1 depending on the specific task.'
lambda (probe amplitude regularization weight) and k (regularization duration) = not reported in main text
The regularization is described as essential for stable convergence, but exact lambda and k values are not given. Fig. S15 caption contains the confusing annotation '(Our parameter set up) (Appropriate loss should be 0)'.
learning rate = 1e-5 to 1e-4
Methods section: 'The learning rate for training the object and probe neural networks ranged from 10^-5 to 10^-4, while the weighting coefficient beta ... varied between 10^-4 and 10^-1 depending on the specific task.'

assumptions (5)

domain assumption The forward model is a Fourier transform of the exit wave product (Fraunhofer far-field, Eq. 1).
Standard ptychography model. The temporal integral in Eq. 1 is not discretized in the described implementation.
domain assumption The probe is single-mode and scan positions are exact.
Stated in the Conclusion: 'this study adopts a single-mode probe assumption' and 'this study assumes that probe positions are accurate'.
ad hoc to paper The object and probe can be represented by the chosen MLP architectures (SIREN object, hash-encoding ReLU probe).
Architecture selection is justified empirically via ablations (Fig. S16), not derived from first principles.
domain assumption The simulation ground truth object is the ePIE reconstruction of a tungsten sample from Cherukara et al.
Sample Preparation: 'we used a subset of the experimental X-ray ptychography dataset from Cherukara et al., where a tungsten calibration sample was reconstructed using the ePIE algorithm.' The 'ground truth' is itself an algorithm output.
ad hoc to paper Probe normalization P <- P/max(Ap) and the regularization term lambda * mean(Ap) guide convergence.
Added specifically to stabilize joint recovery; ablations in Fig. S15 show failure without them.

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Cite this review

Pith. "Pith review of Learning neural representations for X-ray ptychography reconstruction with unknown probes." pith.science (2026). https://pith.science/paper/IBZRUAME

@misc{pith2026250904402,
  author       = {Pith},
  title        = {Pith review of: Learning neural representations for X-ray ptychography reconstruction with unknown probes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IBZRUAME}},
  note         = {Machine review of arXiv:2509.04402}
}

read the original abstract

X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object and probe recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

Figures

Figures reproduced from arXiv: 2509.04402 by the authors.

**Figure 2.** Object and probe reconstruction accuracy across scanning overlap ratios. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Method robustness against noise in probe and object reconstructions. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Comparison of reconstruction performance across different focusing systems and methods. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Exposure time-dependent reconstruction fidelity. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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write newline

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

author Grote, L. et al. title Imaging Cu 2 O nanocube hollowing in solution by quantitative in situ X -ray ptychography . journal Nature Communications volume 13 , pages 4971 ( year 2022 )

work page 2022

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