{"id":"422ef87d-08b9-4d1b-82ea-92d95d233610","arxiv_id":"2507.05647","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Adding a noise-matched rectification step (RNSD+) to mean-reverting SDE sinogram inpainting improves limited-angle CT reconstruction under 5-15 dB Gaussian noise on the synthetic ChromSTET2025 dataset.","lead":"Limited-angle CT scans lose the projections needed for a clean image, and most AI fixers ignore the noise that real machines add. This paper adds a noise-aware correction step, called RNSD+, to a diffusion-based sinogram inpainting pipeline and reports consistent metric gains on a simulated chromatin electron-tomography dataset.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (7) uses incompatible units: with dt=1/T=0.01, γ_t² can be negative while λ_t=1, so RNSD+ is undefined as printed and the schedule's noise-matching guarantee is unverified.","rationale":"The reader and I converge on the same weakest assumption; I agree. The central claim is that RNSD+ improves noisy limited-angle CT by matching inference-time noise to the score model's training envelope. That claim fails if the matching coefficients are dimensionally inconsistent or if γ_t² can be negative. This is an internal consistency check, not a consensus disagreement, and it is directly verifiable from the printed equations plus the reported T=100. I credit the authors for an honest extension and for reporting ten-run averages, but the absence of code, error bars, and external noisy baselines means the numerical gains cannot be independently checked; this is consistent with a conditional verdict. My stress-test concern is narrower: before asking for external baselines, the paper's own rectification schedule should be executable. The concrete arithmetic check would settle whether this concern lands; until it is run, the conditional verdict is the right call.","tokens_in":6951,"tokens_out":7192,"duration_ms":84991,"concrete_test":"Re-derive the update with Euler–Maruyama discretization dt=1/T exactly as stated in Eq. (6). Using T=100, the σ_t schedule from the MR-SDE baseline [10]/[16], h_t from Eq. (7), and σ_y values matching the reported 5–15 dB SNR on 256×256 sinograms, compute γ_t² = σ_t² dt − (h_t λ_t σ_y)² for all t and for β=1. If any γ_t²<0, the published RNSD+ is not implementable at those steps and the Table 1 results require an unreported modification. If all γ_t²≥0, ask the authors for code and rerun Table 1; the numerical claim is then an empirical reproducibility question, not a mathematical one.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the noise-aware rectification in Eqs. (5)-(7). From Eq. (6), d w̄ = √dt σ_t ε_t, so after the measurement correction the per-step noise variance that the score model must absorb is γ_t² dt in the range space, with γ_t² = σ_t² dt − (h_t λ_t σ_y)². This requires σ_t² dt ≥ (h_t λ_t σ_y)². Eq. (7) instead applies λ_t=1 under the much weaker condition σ_t ≥ h_t σ_y, ignoring the √dt factor. With T=100, dt=0.01; whenever h_t σ_y > σ_t/10 the radicand is negative, so the update cannot be executed as written. The text says the coefficients keep measurement noise below the model-trained level σ_t, but the comparison is between different quantities: σ_t is a per-√time SDE coefficient while σ_y is a per-sample noise level. The printed second equality in Eq. (6) also drops the pseudo-inverse A†, and the h_t formula is asserted without derivation. None of this disproves the experiments, but the headline numbers in Table 1 depend on an unverified schedule; if the schedule has hidden rescalings or a different dt convention, they must be reported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses noisy limited-angle CT by formulating it as sinogram inpainting with a Mean-Reverting Stochastic Differential Equation (MR-SDE). It introduces RNSD+, an inference-time rectification that scales the range-space data-consistency correction by a coefficient λ_t and adjusts the injected diffusion noise by a coefficient γ_t, with an additional damping parameter β for robustness to noise-level misestimation. Experiments on the ChromSTET2025 dataset compare FBP, NafNet, MR-SDE without RNSD+, and the proposed method, reporting best sinogram-domain PSNR/SSIM/LPIPS and best image-domain PSNR/LPIPS for RNSD+. A robustness study examines the effect of varying σ_y estimation error and β.","tokens_in":7210,"tokens_out":9681,"duration_ms":103821,"significance":"If the rectification schedule is correct, the paper makes a useful contribution: explicitly accounting for measurement noise at inference time in diffusion-based sinogram completion is a practical need, and the reported gains (e.g., sinogram-domain PSNR 35.91 vs 32.03) are encouraging. The paper is also honest about the role of the estimated noise level and provides a tunable damping factor. However, the central mathematical derivation is not clean as printed: the key equations contain dimensional inconsistencies and an unverified nonnegativity condition. The empirical comparison also leans heavily on the authors' own prior work as the main diffusion baseline. The core idea is plausible and likely fixable, but the paper as printed does not yet provide a verified description of what was implemented.","major_comments":[{"comment":"The second equality in Eq. (6) is algebraically and dimensionally inconsistent as printed. From the first expression, x'_{0|t} = \\hat{x}_{0|t} - λ_t A^†(A \\hat{x}_{0|t} - y) expands to (I - λ_t A^† A) \\hat{x}_{0|t} + λ_t A^† y, not (I - λ_t A) \\hat{x}_{0|t} - λ_t y. Because A ∈ R^{N×M}, the matrix I - λ_t A is not defined, and the printed form drops the pseudo-inverse that defines the range-space projection. Since this rectification is the paper's central contribution and is used in all experiments, the equation must be corrected and the implemented form must be stated unambiguously; the same issue affects Eq. (5), where the symbol x on the right-hand side is undefined.","section":"Section 2.1, Eq. (6)"},{"comment":"The nonnegativity condition for γ_t² is dimensionally mismatched. With d \\bar{w} = √dt σ_t ε_t, the per-step variance of the injected SDE noise is σ_t² dt, whereas the measurement-noise contribution in the range space has variance on the order of (h_t λ_t σ_y)². The condition for γ_t² ≥ 0 is therefore σ_t² dt ≥ (h_t λ_t σ_y)², not σ_t ≥ h_t σ_y as printed. With T = 100, dt = 0.01, whenever h_t σ_y exceeds σ_t/10 the radicand is negative and the update cannot be executed as written. Please report the effective dt convention and the exact implemented schedule, or revise the definitions so that the radicand is guaranteed nonnegative in the reported experiments.","section":"Section 2.1, Eq. (7)"},{"comment":"The claim that the rectification keeps the effective inference-time noise within the score model's trained range is asserted without derivation. In particular, σ_t is a per-√t SDE coefficient while σ_y is a per-sample noise level, so comparing them requires an explicit discrete-time conversion; the distribution of ε_t is written as N(μ, λ²), which is incompatible with d \\bar{w} being a noise increment; and h_t is defined using ζ'_t, which appears identical to \\bar ζ_t introduced in Eq. (3), making the formula ambiguous. A clean derivation of λ_t, γ_t, and h_t, with all distributions and the discrete-time variance of each term, is necessary to verify that the score network is not fed out-of-distribution residual noise.","section":"Section 2.1, Eqs. (6)-(7)"}],"minor_comments":[{"comment":"The table reports 'ten-run average' results without standard deviations or significance tests; given that some image-domain gaps are modest (e.g., PSNR 20.43 vs 19.19), variance information is needed to assess the claim of consistent improvement.","section":"Table 1"},{"comment":"The text refers to 'Figure 2.1'; this should be 'Figure 2'. The heading of Section 3.3, 'Robusteness', should be 'Robustness'.","section":"Section 3.2"},{"comment":"The expression for h_t is ambiguous: ζ'_t appears to be the same as \\bar ζ_t, and the exponent e^{-\\bar ζ_t - 1} is unclear. Please define all quantities explicitly.","section":"Eq. (7)"},{"comment":"The abstract claims generalization 'across varying noise intensity and acquisition scenarios', but the experiments vary noise level and σ_y estimation error only; the missing-angle range and noise type are fixed, so the claim is stronger than what is demonstrated.","section":"Abstract"},{"comment":"Reference [15], which serves as the main baseline, is cited only as '2025' without a venue or arXiv identifier; it should be made identifiable.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about Eq. (7) is valid and should be addressed before further review. I also note that the only diffusion baseline is the authors' own prior work [15], making the comparison somewhat self-referential; an external noisy-LACT baseline or a clearly scoped claim would strengthen the paper. The central idea is plausible and the issues appear fixable within a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"RNSD+ is a real but narrow extension: it takes the range-null-space rectification from the authors' earlier RNSD/MR-SDE work and adds an explicit noise-aware cap on the correction plus a rebalanced noise injection, with the sigma_y dependence appearing in lambda_t, gamma_t, and h_t. That specific schedule is not in [10], [15], [16], or [17], so it is a new result. The experimental direction is plausible and consistent with DDNM-style noise-aware correction results; the robustness sweep over beta and noise-scale mismatch is a useful addition. If the numbers in Table 1 are reproducible, the ~3 dB gain over the no-rectification baseline matters for electron tomography.\n\nThat said, the printed math does not hold up. Eq (6) claims x'_{0|t} = (I - lambda_t A) x_hat - lambda_t y, but the correct expansion is (I - lambda_t A^dagger A) x_hat - lambda_t A^dagger y; as printed the dimensions do not match. That is likely a typo, but it makes the method ambiguous. More seriously, Eq (7) sets lambda_t = 1 when sigma_t >= h_t sigma_y, yet gamma_t^2 = sigma_t^2 dt - (h_t lambda_t sigma_y)^2 requires sigma_t sqrt(dt) >= h_t sigma_y. With dt = 0.01, the radicand goes negative whenever h_t sigma_y > sigma_t/10, so the update is undefined as written. The stress-test note is right: sigma_t is a per-square-root-time SDE coefficient and sigma_y is a per-sample noise level; Eq (7) mixes them. The text asserts the coefficients keep the added noise within the model-trained range, but that is a claim, not a derivation, and the printed condition does not guarantee it.\n\nThe empirical work is also thinner than the abstract implies: the main baseline is the authors' own unpublished MR-SDE [15], no external noisy LACT method is run, there are no error bars, and no code or data are released. The experiment is one synthetic dataset (ChromSTET2025). None of this disproves the results, but the paper currently overclaims generalization.\n\nWho should read this: people working on diffusion-based inverse problems in limited-angle CT. It is worth a serious referee, but only if the referee demands corrected equations, a real derivation of the schedule, external baselines, and code/data. I would send it to review with that expectation, not desk-reject it and not accept it as-is.","headline":"A narrow noise-aware extension of RNSD with promising experiments, but the central schedule as printed has a unit error that makes it undefined; needs major revision before the numbers can be trusted.","tokens_in":7858,"tokens_out":5409,"would_cite":false,"duration_ms":57615,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A noise-aware rectification step makes diffusion-based limited-angle CT reconstruction robust to measurement noise, with roughly 3 dB gains in sinogram-domain PSNR.","keywords":["limited-angle CT","sinogram inpainting","mean-reverting stochastic differential equation","diffusion model","noise-aware rectification","range-null space decomposition","data consistency"],"falsifier":"Measure the variance of the residual $x'_{0|t} - x_0$ at each reverse step under the proposed schedule; if it exceeds the training-time $\\sigma_t$ when the noise level is known exactly, or if the reconstruction quality peaks away from the $\\gamma_t$ values in Eq. (7), the rectification schedule is not doing the work the paper claims.","tokens_in":6615,"feed_emoji":"🩻","tokens_out":7360,"duration_ms":79771,"temperature":0.7,"pith_summary":"Limited-angle CT scans are hard because many projection angles are missing; adding real measurement noise makes the problem harder still. The paper argues that a diffusion model can complete the missing sinogram angles accurately under noise, provided the rectification step is redesigned to fold the measurement noise into the diffusion process instead of pretending it is absent. The proposed RNSD+ correction scales the range-space data-consistency term and adjusts the injected noise at every reverse step, so the total noise level stays inside what the score network was trained to remove. On synthesized noisy chromatin electron-tomography data, the paper reports that RNSD+ beats the non-rectified version of the same model and NafNet in both sinogram and final image metrics, while a damping parameter gives robustness to noise-level mismatch.","feed_headline":"Noise-aware diffusion gains 3 dB on limited-angle CT scans","feed_subtitle":"A rectification step that folds measurement noise into the diffusion process beats prior methods on noisy missing-angle scans.","key_machinery":"The machinery is the mean-reverting stochastic differential equation, whose forward process pulls the state toward the partially observed sinogram as terminal mean $\\mu$, paired with RNSD+ rectification at each reverse step. RNSD+ splits the current estimate into the range space of the measurement operator (what the measurements tell us) and the null space (the missing angles), corrects the range-space part against $y$ with the time-dependent scale $\\lambda_t$, and injects the adjusted noise $n'_t$ with scale $\\gamma_t$ so that the effective residual noise stays within the maximum level the score model can denoise. A damping factor $\\beta \\in (0,1]$ scales down the correction when the noise estimate is uncertain.","core_discovery":"The central claim is that the RNSD+ rectification, replacing Eq. (5) with $x'_{0|t} = \\hat{x}_{0|t} - \\lambda_t A^\\dagger(A\\hat{x}_{0|t} - y)$ and adding the adjusted noise $n'_t = [A\\gamma_t + (I - A)\\sigma_t]\\,d\\bar{w}$, lets a mean-reverting diffusion model complete missing angular views even when the observed sinogram is noisy. In this design the measurement noise is not a nuisance to be filtered out; it is absorbed into the Gaussian noise budget and removed by the score network as the reverse process evolves. The paper's experiments support this by showing that, on the ChromSTET2025 dataset, RNSD+ gives the best PSNR, SSIM and LPIPS among the tested methods in both the sinogram domain and after filtered back projection, including a roughly 3 dB gain over the same model without rectification.","pith_inferences":["Beyond the paper's experiments, the same noise-aware rectification should transfer to other linear inverse problems with Gaussian measurement noise, such as magnetic-resonance reconstruction or deblurring, because the algebra only uses the measurement operator and the noise variance.","A natural testable extension is to replace the known-noise assumption with a lightweight noise estimator and see whether the $\\beta$ damping recovers most of the reported PSNR gains when the estimate is intentionally biased.","The paper's time-travel default suggests the rectification may leave mild artifacts in the early reverse steps; measuring per-step error would show whether the benefit comes from the later stages of denoising."],"forward_implications":["On the tested dataset, adding RNSD+ to the MR-SDE sinogram-completion pipeline improves sinogram-domain PSNR from 32.03 to 35.91 dB, with SSIM rising from 0.911 to 0.950 and LPIPS falling from 0.0300 to 0.0222.","After filtered back projection, the method improves image-domain PSNR to 20.43 dB and LPIPS to 0.1053, ahead of NafNet and the non-rectified baseline, meaning the gains survive the reconstruction step.","A damping factor $\\beta$ lets users trade data consistency for stability when the noise standard deviation is not known exactly, with $\\beta=1$ applying the full correction and smaller values protecting against overestimated noise.","Because the pipeline completes sinograms first and then applies ordinary FBP, it can be dropped into existing limited-angle CT workflows without changing the reconstruction backend.","The framework is stated for Gaussian measurement noise, so it carries over across the tested noise intensities (5–15 dB SNR) and acquisition scenarios used in the experiments."],"supporting_citations":[{"why":"Supplies the residual null-space decomposition rectification scheme that RNSD+ extends to noisy measurements.","marker":"[10]"},{"why":"The authors' earlier MR-SDE sinogram-completion method, used as the no-rectification baseline.","marker":"[15]"},{"why":"Provides the mean-reverting SDE formulation that drives the forward and reverse diffusion.","marker":"[16]"},{"why":"Inspires treating measurement noise as part of the Gaussian noise and supplies the time-travel strategy used by default.","marker":"[17]"},{"why":"Underlies the ChromSTET2025 dataset used for training and testing, i.e., the evidence base for the reported gains.","marker":"[18]"},{"why":"Provides the NafNet baseline and the low-fidelity reconstruction used as auxiliary conditional input.","marker":"[19]"}],"fun_headline_variants":["Diffusion CT absorbs noise, gains 3 dB on limited-angle scans","RNSD+ rectifies noise for robust limited-angle CT","Noise-inclusive diffusion improves noisy CT reconstruction","Mean-reverting diffusion tames noisy limited-angle CT"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the score network trained on the MR-SDE noise schedule can also remove the residual noise left after the measurement-consistent rectification, so the inference-time noise never exceeds the maximum level the model has seen during training.","fun_headline_variants_meta":{"raw":{"variants":["Diffusion CT absorbs noise, gains 3 dB on limited-angle scans","RNSD+ rectifies noise for robust limited-angle CT","Noise-inclusive diffusion improves noisy CT reconstruction","Mean-reverting diffusion tames noisy limited-angle CT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000305,"raw_usage":{"total_tokens":1720,"prompt_tokens":884,"completion_tokens":836,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":500,"completion_tokens_details":{"reasoning_tokens":768}},"tokens_in":500,"tokens_out":836,"duration_ms":10592,"temperature":1.0,"reasoning_tokens":768,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:23:38.629524+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the variance of the residual $x'_{0|t} - x_0$ at each reverse step under the proposed schedule; if it exceeds the training-time $\\sigma_t$ when the noise level is known exactly, or if the reconstruction quality peaks away from the $\\gamma_t$ values in Eq. (7), the rectification schedule is not doing the work the paper claims.","supporting_citations":[{"cited_title":"Generative adversar- ial nets,","cited_arxiv_id":null,"evidence_quote":"Supplies the residual null-space decomposition rectification scheme that RNSD+ extends to noisy measurements."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The authors' earlier MR-SDE sinogram-completion method, used as the no-rectification baseline."},{"cited_title":"Dolce: A model-based probabilistic diffu- sion framework for limited-angle ct reconstruction,","cited_arxiv_id":null,"evidence_quote":"Provides the mean-reverting SDE formulation that drives the forward and reverse diffusion."},{"cited_title":"Rn- sdes: Limited-angle ct reconstruction with residual null- space diffusion stochastic differential equations,","cited_arxiv_id":null,"evidence_quote":"Inspires treating measurement noise as part of the Gaussian noise and supplies the time-travel strategy used by default."},{"cited_title":"Deep learning based sinogram correction for metal artifact re- duction,","cited_arxiv_id":null,"evidence_quote":"Underlies the ChromSTET2025 dataset used for training and testing, i.e., the evidence base for the reported gains."},{"cited_title":"Sinogram image completion for limited angle tomography with genera- tive adversarial networks,","cited_arxiv_id":null,"evidence_quote":"Provides the NafNet baseline and the low-fidelity reconstruction used as auxiliary conditional input."}],"review_version":1}