{"id":"902a2c00-ab07-4f2c-bab1-cfa85c764c8a","arxiv_id":"2512.17561","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Ptychographic phase reconstruction can be decomposed into a sum of precomputed single-electron contributions, enabling linear-complexity, event-wise direct phase retrieval.","lead":"This paper introduces a way to rebuild a ptychographic microscope image by adding one small pre-computed guide patch for every detected electron, instead of processing whole detector frames. If it works, low-dose electron, X-ray, and optical imaging could become much faster and work over larger areas in real time.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Real-time claim rests on exact integer scan-grid alignment; non-grid or drifted positions force FFT shifting, which the paper admits defeats the algorithm's purpose.","rationale":"The reader's weakest assumption correctly identifies the integer-scan-grid requirement as the main practical vulnerability. The derivation of GPRI is linear and mathematically plausible, and the simulations qualitatively support the method. However, the strongest claim of real-time, high-throughput, linear-complexity ptychography depends on the ability to shift precomputed guide functions by exact integer pixel offsets. The paper itself concedes that violating this condition forces FFT shifting and thereby defeats the algorithm's intended advantage, yet it provides no robustness test for realistic scan imperfections. My concern agrees with the reader's and does not move the verdict: conditional acceptance remains appropriate, with the condition that the authors demonstrate equivalence quantitatively and address non-ideal scan grids.","tokens_in":38612,"tokens_out":21888,"duration_ms":216312,"concrete_test":"Run the GPRI-WDD reconstruction on the same simulated poliovirus dataset but with scan positions perturbed by sub-pixel random offsets, e.g., Gaussian sigma = 0.2 reconstruction pixel, or with a slow linear drift. Compare the resulting reconstruction against the ideal integer-grid GPRI result and against a conventional WDD implementation, and measure processing time per event. If the perturbed-grid reconstruction shows significant artefacts or the need for FFT shifting pushes per-event processing time beyond the event-stream bandwidth, the integer-alignment assumption is confirmed as load-bearing.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.1 states that the ratio of scan step to reconstruction pixel must be an integer, and that if it is not, \"FFT-based shifting becomes necessary, which defeats the purpose of the wider algorithm.\" This is a load-bearing practical condition for the headline real-time, linear-complexity, large-field-of-view claim. Equations (20)-(22) implement WDD as a simple shift-and-add of precomputed guide functions; this is exact and O(events) only when every experimental scan position r_s coincides with a fixed integer multiple of the reconstruction pixel. Real event-driven acquisitions are subject to beam drift, fly-back, stage motion, and non-Cartesian scan paths, which produce sub-pixel or non-uniform scan positions. Under those conditions each event would require interpolation or per-event FFT shifting, reintroducing per-event cost and approximation error. The paper provides no simulation or experiment with a non-integer or perturbed scan grid; all demonstrations use a perfectly aligned 144x144 raster. The mathematical equivalence may survive, but the practical central claim is conditional on an idealization. Additionally, the conclusion asserts a result \"identical to that of a conventional WDD implementation\" without showing a quantitative side-by-side comparison, so the claimed exact equivalence is not independently verified in the presented evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces 'guided progressive reconstructive imaging' (GPRI), a reformulation of analytical ptychography in which the reconstruction is built by cumulatively adding precomputed, specimen-independent guide functions, one per detected event or per detector pixel. The derivation starts from the standard WDD relation (Eq. 14), inserts a single-count intensity modeled as a product of Dirac deltas (Eq. 15), and obtains a guide-function library G_WDD_qd(r) (Eqs. 17–18). The whole reconstruction is then expressed as a shift-and-add sum over scan positions and detector events (Eqs. 20–22). The paper claims O(events) complexity, no dense frame storage, progressive/immediate feedback, and identical results to conventional WDD. Validation is by multislice simulations of a poliovirus at doses down to about 10 e⁻/Ų, using a 144×144 perfectly aligned raster. The appendix extends the same library idea to SBI and iCoM.","tokens_in":38902,"tokens_out":5284,"duration_ms":54636,"significance":"The mathematical reduction is elegant and appears internally consistent. If the equivalence to conventional WDD is exact up to normalization and pixelization, the event-wise shift-and-add formulation is a genuinely useful algorithmic insight: it decouples the reconstruction from FFT-based scan-to-frequency transforms and makes the cost linear in the number of events. The precomputed kernel-limited library is a practical strength, and the extension to SBI/iCoM broadens the impact. However, the headline claims of real-time, low-dose, large-field-of-view imaging are only partially supported: the real-time capability is not measured here and is delegated to ref. [33]; the low-dose demonstration is qualitative; and the linear-complexity advantage hinges on an integer-aligned scan raster that is not robust to drift or non-Cartesian scan paths.","major_comments":[{"comment":"This section states that the ratio of the scan step to the reconstruction pixel size 'has to be a integer', and that otherwise 'FFT-based shifting becomes necessary, which defeats the purpose of the wider algorithm.' This condition is load-bearing for the O(events) real-time claim. Real event-driven acquisitions include beam drift, flyback, and non-uniform scan paths, all of which produce scan positions that are not exact integer multiples of the reconstruction pixel. No simulation or experiment with a perturbed, drifted, or non-Cartesian raster is presented; the only demonstration is a perfectly aligned 144×144 grid. The authors should either provide a quantitative analysis of the cost and accuracy of an interpolation/FFT fallback, or explicitly restrict the real-time/linear-complexity claims to integer-aligned rasters.","section":"§3.1"},{"comment":"The conclusion claims 'a result identical to that of a conventional WDD implementation was obtained', but this is not supported by the evidence shown. Figure 4 displays GPRI reconstructions for several doses, but no side-by-side comparison with a conventional WDD reconstruction of the same simulated data, no difference map, and no error metric (e.g., SSIM, RMS error, or Fourier ring correlation) are provided. Since exact equivalence is a central claim, a quantitative comparison should be supplied.","section":"Conclusion and §3.3"},{"comment":"The dose-efficiency conclusion rests on visual inspection of Fig. 4. The text states that results show 'the same stability against noise as demonstrated by existing workflows', but no quantitative comparison with conventional WDD, SBI, or iterative methods is made. Likewise, the real-time throughput claim ('processing speed high enough to surpass the acquisition bandwidth', §4.2) is not measured anywhere in this manuscript; it is delegated to ref. [33]. Please include at least a timing/memory benchmark of the GPRI update loop, or soften the claims to statements about algorithmic complexity.","section":"§3.3 and §4.2"},{"comment":"The pattern-wise normalization in Eq. (20) divides by n(r_s), the number of counts at scan position r_s. In the low-dose regime that is central to the paper, many scan positions will have n(r_s)=0, and the formula as written is undefined there. The authors should specify the convention for empty scan positions (e.g., omit them from the sum or define 0/0=0) and demonstrate that this convention does not bias the result.","section":"Eqs. (20) and (21)"}],"minor_comments":[{"comment":"'the ratio of the scan step over it has to be a integer' should read 'an integer'.","section":"§3.1"},{"comment":"The sentence 'thus by a simple summation of individual qd-selected and rs-shifted guide functions G_WDD_qd(r), was also devised in subsection 1.3' is grammatically incomplete; please revise for clarity.","section":"§2.4"},{"comment":"'The exception is the case of a)' should be 'the case of panel (a)'.","section":"Fig. 3 caption"},{"comment":"The notation \\tilde{G}^{SBI}_{q_d}(r) mixes Fourier-domain tilde notation with a real-space argument r. Please clarify which quantity is defined in which space.","section":"Appendix, Eqs. (25) and (27)"},{"comment":"The claim that 'an additive cumulation of the contributions then leads to the same result as a collective treatment' is introduced before the WDD-specific definition of ΔT. It would help to state explicitly the class of reconstruction operators for which this linearity holds.","section":"§1.3, Eq. (4)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript leans on same-group references [33,40] and its own patent [100] for performance and parameter claims. This is not improper, but the manuscript would be substantially stronger if the real-time and equivalence claims were supported by self-contained benchmarks. The integer-grid limitation and the absence of a quantitative comparison with conventional WDD are the main reasons I recommend major revision rather than minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea is real: WDD (and SBI/iCoM) can be rewritten as a sum of precomputed, specimen-independent guide functions, one per detection event. The derivation in Section 2 is elementary but correct, and the extension to SBI and iCoM in the appendix is a nice bonus. The low-dose simulation on poliovirus is plausible and suggests the method works. This is the first time I've seen the count-wise decomposition of direct ptychography written out explicitly, and the linear-complexity claim is, in principle, a big deal for event-driven detectors.\n\nThat said, the paper oversells itself in a few places. The conclusion says the result is \"identical to that of a conventional WDD implementation,\" but no side-by-side comparison is shown. The simulations demonstrate qualitative feasibility, not numerical equivalence. Noise performance is described only in words; there are no SNR or transfer-function curves. Real-time throughput is outsourced to the authors' own companion paper [33] and patent [100], with no benchmarks in this manuscript. None of that is fatal, but it means the strongest claims are currently unverified.\n\nThe more substantive concern is the integer scan-grid condition. Section 3.1 admits that if the ratio of scan step to reconstruction pixel is not an integer, FFT-based shifting becomes necessary, \"which defeats the purpose of the wider algorithm.\" That is a load-bearing premise for the O(events) real-time claim. Real event-driven acquisitions have drift, fly-back, and non-Cartesian scan paths; the paper gives no simulation or experiment with a perturbed grid. The mathematical equivalence in Eqs. (20)-(22) survives regardless, but the practical headline is conditional on an idealization that the authors themselves flag. I'd call this a genuine practical limitation, not a mathematical flaw.\n\nAlso, no code or data are released, which makes the simulations hard to check independently. The heavy reliance on the authors' own prior work is not damning, but it does mean the performance claims should be treated as self-referential until independently reproduced.\n\nWho is this for? People working on direct ptychography with event-driven detectors, especially low-dose STEM. The framework is likely to be useful even with the integer-grid caveat, since many STEM rasters are regular. The paper deserves a serious referee. I'd recommend conditional acceptance: require a numerical equivalence check against conventional WDD, noise statistics, and either an event-driven experiment or a simulation with a drifted/non-grid scan before the strong version of the real-time claim is accepted.","headline":"Sound and novel event-wise reformulation of WDD, but the real-time linear-complexity claim rides on an integer scan grid the paper acknowledges is fragile, and the asserted identity to conventional WDD is never demonstrated numerically.","tokens_in":39411,"tokens_out":2010,"would_cite":true,"duration_ms":25156,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that direct ptychographic phase retrieval reduces to a linear shift-and-add of precomputed guide functions, one per detected electron.","keywords":["ptychography","event-driven detection","Wigner distribution deconvolution","phase retrieval","low-dose electron microscopy","guide functions","real-time imaging","Timepix"],"falsifier":"Run a WDD reconstruction on an experimental dataset acquired with an event-driven detector on a non-integer or distorted scan grid, and compare the GPRI result with a conventional WDD reconstruction from the same events. If the two diverge by more than numerical precision without FFT-based interpolation, or if the processing time no longer scales linearly with event count, the central equivalence claim fails in practice.","tokens_in":38491,"feed_emoji":"🔬","tokens_out":4051,"duration_ms":40470,"temperature":0.7,"pith_summary":"The paper's central claim is that ptychographic reconstruction — recovering a specimen's phase and amplitude from overlapping scattered-intensity measurements — can be reformulated as a strictly additive process over individual detection events. Instead of storing dense diffraction frames and Fourier-transforming the whole dataset, each detected electron contributes a fixed, precomputed 'guide function' shifted to its scan position, and the reconstruction is just the cumulative sum. The authors prove this for the Wigner distribution deconvolution (WDD) method, and provide equivalent formulations for sideband integration and integrated center-of-mass imaging. If correct, this turns direct ptychography into an O(events) operation with no dense-frame storage, making real-time, low-dose phase imaging feasible on event-driven detectors and easing large-field-of-view scans.","feed_headline":"One electron at a time: ptychography becomes a shift-and-add sum","feed_subtitle":"Direct phase retrieval reduces to adding precomputed kernels per detected event, enabling real-time low-dose imaging.","key_machinery":"The load-bearing object is the guide-function library G_qd(r): a set of kernel-limited, complex-valued distributions, one per detector pixel, precomputed from the probe's Wigner distribution (aperture, aberration, wavelength) and the detector MTF via a Wiener-filtered inversion. Each detected event contributes one such kernel shifted to the event's scan position; the whole reconstruction is the cumulative sum, with a normalization by the number of counts per scan position. This converts the conventional work of Fourier-transforming full frames and deconvolving in phase space into a per-event table lookup and addition, giving linear complexity in the number of events and decoupling the recons","core_discovery":"On the paper's own terms, the core discovery is that a single count at detector pixel qd and scan position rs contains enough information to update the reconstruction by a known, specimen-independent quantity: the contribution equals G_qd(r − rs), where G_qd is derived solely from the known illumination (aperture, aberrations, wavelength) and the detector's modulation transfer function. Because the WDD reconstruction is linear in the intensity, summing these contributions event-by-event reproduces exactly the result of the conventional collective Wigner-deconvolution treatment. The paper derives the guide-function library in Eq. (18), shows the summation forms in Eqs. (20)–(22), and verifies","pith_inferences":["Editorial extension: the shift-and-add structure suggests that any linear direct-reconstruction scheme could be compiled into a kernel library, so future instrument-specific optimizations could be pushed entirely into library precomputation.","Editorial extension: because each event contributes independently, the approach naturally supports streaming and distributed processing across many cores without inter-event communication — a property the paper notes but does not demonstrate.","Editorial extension: the integer-scan-step restriction implies the practical payoff depends on scan-raster fidelity; combining the method with live scan-position correction (via beam-current or drift monitoring) would be a direct testable extension.","Editorial extension: the guide-function profiles show that near-aperture scattering vectors carry the most noise-robust information, which quantifies which detector annuli matter most for low-dose experiments and could guide detector design."],"forward_implications":["A WDD ptychographic reconstruction can be produced progressively as events arrive, so the estimate improves continuously and can be displayed in real time during acquisition.","Because the library is specimen-independent, the same precomputed kernels serve any dataset acquired under the same illumination, eliminating per-dataset heavy transforms.","Reconstruction cost scales linearly with the number of events and scan positions, removing the nonlinear N² or N log N bottleneck that limits field of view in direct ptychography.","The method admits count-wise, frame-based, or hybrid data formats through the same additive pipeline, and extends to sideband integration and integrated center-of-mass imaging.","Low-dose performance matches conventional direct approaches: interpretable contrast is demonstrated in simulation down to about 10 e−/Ų."],"fun_headline_variants":["Ptychography becomes a real-time sum of precomputed kernels","Low-dose ptychography: just add each photon's kernel","Shift-and-add ptychography: real-time from single events","Ptychography in real time: each event simply adds a kernel","Event-wise ptychography: low-dose, real-time reconstruction"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The strongest practical premise is that the scan raster consists of a uniform grid whose step is an integer multiple of the reconstruction pixel; if real scan positions drift off this grid (microscope distortions, beam drift, fly-back, or non-grid scans), the fast shift-and-add path breaks down and the method loses its real-time advantage.","fun_headline_variants_meta":{"raw":{"variants":["Ptychography becomes a real-time sum of precomputed kernels","Low-dose ptychography: just add each photon's kernel","Shift-and-add ptychography: real-time from single events","Ptychography in real time: each event simply adds a kernel","Event-wise ptychography: low-dose, real-time reconstruction"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001515,"raw_usage":{"total_tokens":5924,"prompt_tokens":779,"completion_tokens":5145,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":523,"completion_tokens_details":{"reasoning_tokens":5057}},"tokens_in":523,"tokens_out":5145,"duration_ms":35221,"temperature":1.0,"reasoning_tokens":5057,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T15:13:16.621023+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a WDD reconstruction on an experimental dataset acquired with an event-driven detector on a non-integer or distorted scan grid, and compare the GPRI result with a conventional WDD reconstruction from the same events. If the two diverge by more than numerical precision without FFT-based interpolation, or if the processing time no longer scales linearly with event count, the central equivalence claim fails in practice.","supporting_citations":[],"review_version":1}