{"id":"38885be3-f059-4461-abb9-d16d5353fcea","arxiv_id":"2608.13159","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A Gaussian-splatting CBCT reconstruction that models polychromatic X-ray spectra and jointly calibrates the system response, reducing metal beam-hardening artifacts without metal masks or known spectra.","lead":"This paper combines Gaussian splatting with a physics-based polychromatic X-ray model to reduce metal-induced beam hardening artifacts in cone-beam CT scans. It jointly reconstructs the 3D volume and calibrates the X-ray spectrum, removing the need for manual metal masks, and reports faster, higher-quality results than prior neural methods on synthetic and real scans.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Real-world superiority claim is not quantitatively established: no PSNR/SSIM is reported for any real scan despite available metal-free references, so the abstract's strongest claim currently rests on selected visual slices.","rationale":"Good-faith reading: the method is a sensible extension of R2-Gaussian, the spectral model is plausible, and the synthetic experiments and NIST check are helpful. The reader's identified assumption about the two-parameter system response is a genuine theoretical risk, but it is partly mitigated by Table 2, where the same model works across filters, detectors, and voltages, and by the MC-based validation in Section 5.1. The most load-bearing weakness is not a single equation but the empirical support for the real-world half of the headline: the paper has reference scans but no real-data metrics. Since the accepted verdict is already CONDITIONAL, my concern does not move the verdict; it sharpens the conditions: either provide quantitative real-data evaluation against those references, or explicitly limit the claim to qualitative improvement on real scenes.","tokens_in":19805,"tokens_out":11252,"duration_ms":111767,"concrete_test":"Use the existing real dataset: for Walnut, Chicken, Bell Pepper, and Broccoli, rigidly register each reconstruction to its metal-free FDK reference, mask metal regions, and compute volume-wise PSNR/SSIM (and per-slice means with standard deviations) for FDK, LIMAR, NMAR, Polyner, Park et al., and Ours. For Metal Rods, use the simulated artifact-free volume as reference. If Ours does not exceed Polyner and Park et al. by a consistent margin on these metrics, the abstract's real-world outperformance claim should be weakened to synthetic-only or qualitative evidence.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim is that the method outperforms state-of-the-art approaches on both synthetic and real-world datasets. The synthetic claim is supported by Table 3, but the real-world claim is supported only by qualitative slices and the NIST attenuation comparison on one phantom. Supplementary Section 7 states: 'Since there is no proper GT available for the real dataset, we do not conduct quantitative evaluations, but qualitative comparison evaluations are done instead.' This is a missing support for the strongest part of the abstract: reconstruction accuracy is an accuracy claim, and without per-volume numbers against the metal-free reference scans that Section 6.3 describes, real-data superiority is not established. It remains possible that the method is better on the displayed slices but not in aggregate, or that the comparison is affected by slice selection. This is load-bearing because the claimed practical contribution is precisely that the self-calibrating model transfers to real hardware.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a Gaussian-splatting CBCT reconstruction method that explicitly models polychromatic X-ray attenuation and self-calibrates the system response. Each Gaussian carries two densities, a constant Compton-like term rho^a and a photoelectric-like term rho^b / E_bar^3 (Eqs. 7-9), and the forward projector (Eqs. 10-12) integrates over normalized energy with a two-parameter piecewise-linear/plateau response (Eq. 6). The Gaussian parameters and the system-response parameters r and E_th are optimized jointly, without requiring metal masks or known spectra. The method is validated on simulated Lung/Teeth/Broccoli volumes (Table 3), on real scans of a walnut, metal rods, chicken, bell pepper, and broccoli (Figs. 8-9), on an OpenGATE Monte-Carlo projection comparison (32.94 dB), on a NIST attenuation comparison, and through ablations. The paper reports 15-30 minute runtimes and releases new datasets.","tokens_in":19931,"tokens_out":6191,"duration_ms":54600,"significance":"If the claims hold, the contribution is significant: this is the first splat-based treatment of beam hardening in CBCT, it removes the need for manual metal masks and spectral calibration, and the core derivation and ablation cleanly attribute the main gain to the polychromatic attenuation model (Lung: baseline 20.68 -> with attenuation model 27.73 -> with both modules 29.19). The OpenGATE validation and the NIST comparison are good-faith checks, and the supplied gradient derivations and GPU-memory measurements support reproducibility. However, the real-world superiority claim currently rests on qualitative slices, and the synthetic evaluation is partly in-domain, so the abstract's strongest claims are not yet fully supported.","major_comments":[{"comment":"The abstract claims \"extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms ... in artifact suppression and reconstruction accuracy,\" but no quantitative metric is reported for any real scan. Supplementary Section 7 states: \"Since there is no proper GT available for the real dataset, we do not conduct quantitative evaluations, but qualitative comparison evaluations are done instead.\" This directly undercuts the load-bearing real-data accuracy claim. Since Section 6.3 reports that every real scene except Metal Rods was also scanned without metal to serve as a reference, the authors could compute volume-level PSNR/SSIM against those metal-free proxies outside the metal-inserted regions, following standard MAR evaluation practice. Without such numbers, the visual comparisons in Figures 1, 8, and 9 may be affected by slice selection and display windowing, and the real-data claim in the abstract remains unsupported.","section":"Section 6.3 and Supplementary Section 7"},{"comment":"The synthetic test data are produced by the same polychromatic Beer-Lambert integral and the same spectral approximations that the method uses for reconstruction, so the large margins in Table 3 (e.g., Lung PSNR 29.19 vs. 20.43 for Polyner) are partly in-domain. The OpenGATE Monte-Carlo validation (PSNR 32.94 dB between projections) is a useful independent check of the simulator, and Table 2 shows robustness across kV/filter/detector choices, but all of Table 2's response variants still lie within the linearly-decaying-plus-plateau family of Eq. (6). The paper should add a test in which the projections are generated by an independent Monte-Carlo simulator with a spectrum containing, for example, characteristic peaks or a thicker filter than the approximation family, and report reconstruction PSNR/SSIM; alternatively, the synthetic claims should be described explicitly as in-domain, with the real-data evidence carrying the generalization claim.","section":"Section 5.1 and Table 3"},{"comment":"The self-calibration claim rests entirely on the faithfulness of the two-parameter response model, yet Table 1 only compares this model with GMM and free-parameter alternatives on the synthetic Lung scene, which was generated by the same simulator family. Section 4.2 justifies the model by neglecting characteristic peaks, assuming a thin filter, and approximating the detector sensitivity as linear; Section 8 concedes that the method relies on approximations of the system response and material attenuation models. A concrete test is needed: either a real measured spectrum, or a synthetic spectrum with characteristic peaks and/or a 1-2 mm filter, run through the optimizer, with the recovered r and E_th compared against the true spectrum. Without such a test, the \"self-calibrating system response\" is only shown to fit the model's own assumptions, and the generalization to real hardware is not established quantitatively.","section":"Section 4.2, Eq. (6), and Table 1"}],"minor_comments":[{"comment":"The main text states that all real acquisitions used a 0.5 mm aluminum filter, but Supplementary Table 2 lists 1.0 mm Al for Walnut and Chicken (Wire). Please reconcile this discrepancy, since the system-response calibration depends on the filter thickness.","section":"Section 6.1 vs. Supplementary Table 2"},{"comment":"The evaluation protocol says PSNR is measured excluding the metal-mask area, but Section 6.2 and Table 3 do not specify how the metal region was defined. Please state the mask-exclusion rule and confirm that the same rule was applied to all baselines.","section":"Supplementary Section 7 and Table 3"},{"comment":"The real attenuation comparison against NIST is reported at the single center energy of 50 keV for water and aluminum. Given the polychromatic model, reporting the reconstructed mu over the full energy range, or at least at two energies, would better substantiate the claim of real attenuation estimation.","section":"Section 5.4"},{"comment":"The colorbars are repeated in each panel and the intensity ranges differ across methods; adding a shared colorbar and stating the display windowing would strengthen the qualitative comparison.","section":"Figures 8-9 and Supplementary Figures 4-6"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for the venue and the core derivation is sound. I would not reject on circularity grounds alone because the OpenGATE validation partially mitigates the concern, but the abstract's real-data accuracy claim must either be backed by quantitative evaluation against the available metal-free reference scans or be softened. The model-mismatch experiment I request in the major comments is, in my view, the most decisive next step for the self-calibration claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Kiseok Choi et al. have written a genuinely useful paper. The core idea—marrying a polychromatic Beer-Lambert forward model with per-Gaussian photoelectric/Compton densities and a jointly optimized two-parameter system response inside R2-Gaussian—is new, and it works. The derivation in Eq. (10) is correct, the ablation isolates the attenuation model as the main contributor (20.68 to 29.19 PSNR on Lung), and the runtime advantage over Polyner and Park et al. (roughly 4–8x) is real. I also respect the Monte-Carlo validation of the synthetic generator (32.94 dB against OpenGATE) and the NIST attenuation check on the real phantom. These give the method more external support than the average within-subfield paper.\n\nThe weaknesses are real but mostly addressable. The largest is that the real-data superiority claim in the abstract is not quantitatively established. The supplementary admits there is no GT for the real datasets, so they rely on qualitative slices, even though they scanned most specimens with and without metal and could have computed PSNR/SSIM against those metal-free references. The synthetic numbers, while impressive, are partly in-domain: the simulator uses the same polychromatic Beer-Lambert integral and similar spectral approximations as the method, so the gain partly reflects model match. The baseline comparisons also carry some risk—Polyner and Park are re-implemented, and ACDNet/DICDNet/OSCNet are applied slice-wise to FDK volumes—though the Discussion is honest about this. There are no error bars anywhere, and I could not find a code or data link in the text despite the abstract promising dataset release.\n\nThe system-response assumption (linear decay into a plateau) is a simplification, but the ablation in Table 1 shows it beats GMM and free-parameter alternatives, so I would not call it a fatal flaw. The claim of needing no spectral priors is slightly overstated—they require Emax and assume a 10 keV floor—but that is a minor tightening.\n\nNet: I would accept this for peer review. The method is plausible, efficient, and well-grounded, and the evaluation gaps are fixable with real-data metrics, error bars, and code release. The abstract should be reined in before publication. If you are working on MAR or splat-based reconstruction, this is worth reading now; otherwise wait for the revised version.","headline":"Solid splat-based polychromatic CBCT reconstruction with a correct core derivation and real speed gains, but the real-data superiority claim rests on qualitative slices until quantitative metrics are added.","tokens_in":20540,"tokens_out":2617,"would_cite":true,"duration_ms":22826,"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":"A splat-based polychromatic model can remove metal beam-hardening streaks from cone-beam CT while reconstructing the volume, without masks or spectrum priors.","keywords":["cone-beam CT","metal artifact reduction","beam hardening","Gaussian splatting","polychromatic forward model","system response self-calibration","photoelectric attenuation","CBCT reconstruction"],"falsifier":"Measure the X-ray spectrum of a scanner with a spectrometer (or scan a phantom with a known k-edge material such as a barium or lead foil) and compare it to the best-fit two-parameter response recovered by the method; if the true spectrum shows peaks or edges that the linear-decay-plateau family cannot express, the method's reconstructed attenuation coefficients will deviate systematically from NIST reference values and residual streak artifacts should reappear.","tokens_in":19536,"feed_emoji":"🩻","tokens_out":11566,"duration_ms":88237,"temperature":0.7,"pith_summary":"This paper claims that the dark streaks and cupping artifacts of metal-induced beam hardening in cone-beam CT can be removed by replacing the monochromatic forward model used in Gaussian splatting with an energy-aware polychromatic one. Each Gaussian carries two densities: a constant Compton density and a photoelectric density that scales as $\\bar{E}^{-3}$, and a global two-parameter system response $\\eta(\\bar{E})$ is optimized together with the volume, so no metal masks, known spectra, or paired training data are needed. It reports higher 3D PSNR and SSIM than FDK, LIMAR, NMAR, Polyner, the fan-beam neural baseline, and learning-based baselines on three synthetic phantoms, and qualitatively cleaner reconstructions on five real CBCT scans. It also runs in roughly 15 to 30 minutes per scan, about an order of magnitude faster than the compared neural representation baselines. If the claims hold, physics-based beam-hardening correction becomes practical on commodity GPUs.","feed_headline":"Gaussian splats erase metal streaks in cone-beam CT","feed_subtitle":"A polychromatic model with self-calibrated spectrum beats prior baselines and runs in minutes per scan.","key_machinery":"The load-bearing object is the discrete polychromatic forward projector, Eqs. (11)-(12): $P(\\hat{x}) = \\sum_i w_i(\\hat{x})\\rho^a_i - \\log \\sum_{k=0}^{N-1} \\eta_k \\exp(-E_k^{-3} \\sum_i w_i(\\hat{x})\\rho^b_i)$. Because the Compton term is energy-independent, it factors out of the exponential, leaving a monochromatic line integral plus an integral over the spectral response applied only to the photoelectric term. The system response $\\eta(\\bar{E})$ is modeled as a soft piecewise function: a linear decay into a constant plateau, with two trainable parameters (threshold $\\bar{E}_{th}$ and intensity ratio $r$). This simple family is chosen to avoid overfitting and to keep self-calibration stable; jointly optimizing it with the Gaussian parameters eliminates the need for spectrum priors and metal masks.","core_discovery":"The central claim is that beam hardening can be corrected jointly with reconstruction by endowing each Gaussian primitive with two energy-dependent densities — a constant Compton component $\\rho^a_i$ and a photoelectric component $\\rho^b_i / \\bar{E}^3$ — and by fitting a global, two-parameter system response $\\eta(\\bar{E})$ whose only free parameters are the threshold energy and the plateau ratio. Putting these into the Beer-Lambert integral separates the Compton line integral from the energy integral, stabilizing the optimization. The same optimization adapts the Gaussian positions, covariances, and densities from FDK-based initialization, and the final volume is evaluated from the fitted Gaussians. On the three synthetic phantoms and five real scans tested, the method claims state-of-the-art artifact suppression and higher reconstruction accuracy than the baselines, while recovering attenuation coefficients for water and aluminum that match the NIST database at the center energy. This is presented as the first splat-based beam-hardening reduction method for CBCT.","pith_inferences":["Editorial inference: because each Gaussian carries separate Compton and photoelectric densities, the same forward model could be extended to estimate material maps or to exploit dual-energy acquisitions, although the paper does not develop material decomposition.","Editorial inference: the fitted threshold and ratio parameters could act as a cheap spectrum sanity check; a drift between scans of a nominally stable tube would flag source or detector change, a use the paper does not mention.","Editorial inference: the two-parameter response family is linear-decay-to-plateau, so spectra with characteristic peaks or k-edges would push the self-calibration outside its representational range and should leave residual artifacts; a direct test would be scanning through a high-Z filter with a known k-edge.","Editorial inference: because no mask is required, the method may transfer to beam-hardening from dense bone, contrast agents, or other high-attenuation materials where a metal mask is hard to define, though only metallic inserts are tested here."],"forward_implications":["On the tested data, metal artifact suppression and volume fidelity improve over classical, learning-based, and physics-based baselines in the reported PSNR3D and SSIM3D metrics.","No metal mask or spectral prior is needed, so the same pipeline applies to new scan geometries and objects without retraining or manual annotation.","Per-scene runtime of roughly 15 to 30 minutes on an RTX A6000 makes the approach about an order of magnitude faster than the compared neural-rendering methods.","The method's reconstructed attenuation values for homogeneous water and aluminum regions agree with NIST reference coefficients, suggesting the corrected volumes are also quantitatively calibrated.","Release of synthetic and real CBCT datasets with severe metal artifacts gives the community standard test scenes for artifact-resilient reconstruction."],"supporting_citations":[{"why":"Supplies the Gaussian splatting reconstruction framework (R2-Gaussian) that the method extends from monochromatic to polychromatic forward projection.","marker":"[ZLC∗24]"},{"why":"Provides the standard analytic baseline and the initial reconstruction volume from which Gaussian primitives are seeded.","marker":"[FDK84]"},{"why":"Polyner, the physics-based neural baseline that assumes a known spectrum; it is the closest comparison for self-calibration without spectral priors.","marker":"[WCW∗23]"},{"why":"Park et al., the implicit-neural-representation baseline for beam-hardening reduction that the paper re-implements in cone-beam geometry.","marker":"[PSJ]"},{"why":"Defines the system response as the product of source spectrum, filter transmission, and detector sensitivity, motivating Eq. (6).","marker":"[CAS∗19]"},{"why":"Justifies the two-component attenuation model: photoelectric dominance at low energy with $\\bar{E}^{-3}$ dependence and an approximately constant Compton term.","marker":"[Spr12]"},{"why":"NIST attenuation coefficients used to validate that reconstructed linear attenuation values for water and aluminum are physically plausible.","marker":"[SHS88]"},{"why":"Supplies the TIGRE-based synthetic CBCT projection generator used to create the realistic polychromatic evaluation scenes.","marker":"[BDHS16]"},{"why":"Provides the XrayPhysics spectrum generation used in synthetic projection and Monte-Carlo validation.","marker":"[KC23]"}],"fun_headline_variants":["Splat-based CBCT kills beam hardening with self-tuned spectrum","Polychromatic splats remove metal streaks without masks","Self-calibrating splats erase CBCT metal artifacts","First splat method to fix beam hardening in cone-beam CT","Gaussian splats learn X-ray spectrum to fix metal artifacts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the true X-ray system response—source spectrum, filter, and detector sensitivity combined—can be adequately represented by a soft linear decay into a constant plateau with only two free parameters; if the real system's response has structure outside that family, such as characteristic emission peaks, a thick filter, or strong energy-dependent detector nonlinearity, the self-calibration cannot recover it and beam-hardening correction will be incomplete.","fun_headline_variants_meta":{"raw":{"variants":["Splat-based CBCT kills beam hardening with self-tuned spectrum","Polychromatic splats remove metal streaks without masks","Self-calibrating splats erase CBCT metal artifacts","First splat method to fix beam hardening in cone-beam CT","Gaussian splats learn X-ray spectrum to fix metal artifacts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000268,"raw_usage":{"total_tokens":1633,"prompt_tokens":974,"completion_tokens":659,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":590,"completion_tokens_details":{"reasoning_tokens":575}},"tokens_in":590,"tokens_out":659,"duration_ms":5939,"temperature":1.0,"reasoning_tokens":575,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:26:55.003523+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the X-ray spectrum of a scanner with a spectrometer (or scan a phantom with a known k-edge material such as a barium or lead foil) and compare it to the best-fit two-parameter response recovered by the method; if the true spectrum shows peaks or edges that the linear-decay-plateau family cannot express, the method's reconstructed attenuation coefficients will deviate systematically from NIST reference values and residual streak artifacts should reappear.","supporting_citations":[],"review_version":1}