Splat-based Metal Artifact Reduction in Cone-Beam CT via Polychromatic Modeling

Abstract: Cone-beam computed tomography (CBCT) enables volumetric reconstruction from X-ray projections, but suffers from severe artifacts--especially beam hardening--when imaging materials with high attenuation such as metals. These artifacts arise from the polychromatic nature of X-rays and are not properly addressed by conventional monochromatic reconstruction algorithms. While recent neural representation-based methods offer improved reconstruction quality, they are computationally expensive and often impractical for deployment. We propose a novel physics-inspired, self-calibrating metal artifact reduction method that efficiently reconstructs 3D CBCT volumes while correcting beam hardening artifacts. Our method integrates a polychromatic X-ray projection model, material-dependent attenuation profiles, and system response modeling into a Gaussian Splatting framework. Unlike prior work, we eliminate the need for manual metal masks or strong prior assumptions, and we optimize both reconstruction parameters and X-ray spectral characteristics jointly during training. We further introduce a high-fidelity synthetic CBCT dataset generation pipeline validated on Monte-Carlo x-ray simulation toolbox and release new datasets with severe metal-induced artifacts to support the community. This is the first splat-based method for reducing beam hardening in CBCT. Extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art approaches in artifact suppression and reconstruction accuracy.

• The paper introduces the first splat-based CBCT beam-hardening reduction method, jointly optimizing a Gaussian attenuation field and a compact two-parameter X-ray system response without metal masks or paired training data.
• The method achieves up to 29.19 dB PSNR and 0.995 SSIM on synthetic scenes, outperforming FDK, NMAR, Polyner, and other baselines while delivering the largest gains in severe-artifact cases.
• The approach reconstructs scenes in roughly 16–31 minutes—substantially faster than neural-field alternatives—but still requires the maximum photon energy and further validation on clinical CBCT data.

Overview

This paper addresses metal-induced beam hardening artifacts in cone-beam computed tomography (CBCT) by embedding a polychromatic X-ray forward model into a differentiable Gaussian Splatting (GS) reconstruction framework. The method, built on R²-Gaussian (Finkelberg et al., 2024), jointly optimizes the attenuation volume and the X-ray system response without requiring metal masks, paired training data, or prior spectral calibration. The authors state this is the first splat-based method for beam hardening reduction in CBCT. Beyond the algorithmic contribution, the paper introduces a synthetic CBCT dataset generation pipeline validated against Monte Carlo simulation and releases new datasets with severe metal artifacts.

Motivation and relation to prior work

Beam hardening arises because real X-ray sources are polychromatic: low-energy photons are preferentially absorbed, so measured projections violate the monochromatic Beer-Lambert model assumed by FDK and most iterative methods. In CBCT this is aggravated by wide cone angles and scatter, producing dark streaks, cupping, and geometric distortion that also degrade downstream segmentation.

Existing approaches fall into three groups. Sinogram interpolation methods such as LIMAR and NMAR depend on accurate metal mask segmentation. Supervised networks (ADN, DICDNet, ACDNet, OSCNet, InDuDoNet) require paired data and masks, limiting generalization; notably, in the paper's real-data experiments these methods fail outright due to out-of-distribution issues. Physics-motivated reconstruction methods—Polyner (NeRF-style energy-dependent attenuation assuming a known spectrum) and Park et al. (linear attenuation under fixed-energy assumptions)—avoid some priors but rely on computationally expensive neural volumetric representations or are restricted to fan-beam geometries. R²-Gaussian offers an efficient explicit Gaussian representation but assumes a monochromatic model, which is precisely the assumption the present work removes.

Method

The framework extends R²-Gaussian's anisotropic Gaussian attenuation field with two physics-inspired components.

System response model. Rather than estimating a free-form spectrum, the authors derive a soft piecewise approximation $\eta(\bar{E})$ combining a linearly decaying region with a constant plateau at high energies, motivated by the Bremsstrahlung spectrum, detector sensitivity decay, and the observation that high-energy spectral components are nearly indistinguishable to gradient-based optimization. Only two parameters ($r$ and threshold $\bar{E}_{th}$) are optimized. An ablation shows this parsimonious model outperforms more flexible alternatives—a 5-component Gaussian mixture (26.51 dB PSNR3D) and fully free parameters (27.74 dB)—reaching 29.19 dB on the Lung scene, supporting the claim that reduced model complexity mitigates overfitting.

Polychromatic attenuation model. Each Gaussian's density is decomposed as $\rho_i(\bar{E}) = \rho_i^a + \bar{E}^{-3}\rho_i^b$, corresponding to a Compton term approximated as constant (justified for photon energies below 120 keV) and a photoelectric term with inverse-cubic energy dependence. This decomposition allows the Compton contribution to be factored out of the exponential in the forward projection, which the authors identify as important for numerical stability during optimization. The energy integral is discretized over $N=15$ components.

Optimization minimizes an $L_1$ plus SSIM loss on log-transformed projections, jointly updating all Gaussian parameters and the system response parameters. Initialization follows R²-Gaussian: FDK pre-reconstruction, 50,000 sampled Gaussians, with $\rho_a$ and $\rho_b$ initialized at 7.5% and 0.75% of voxel intensity respectively.

Validation of components

The synthetic projection simulator (built on TIGRE, extended to polychromatic CBCT with Poisson and Gaussian noise) was validated against OpenGATE/Geant4 Monte Carlo simulation using one billion particles, achieving 32.94 dB PSNR agreement—strong evidence that the training data distribution matches physically realistic polychromatic acquisition. Cross-hardware generalization tests across voltages (60–120 kV), filters (Al, Cu), and detectors (GOS, CsI) show consistent performance between roughly 28.9 and 31.2 dB PSNR3D, indicating the self-calibrating response model does not overfit a single acquisition configuration. Reconstructed attenuation values for water and aluminum segments align well with NIST reference coefficients at 50 keV, supporting quantitative rather than merely perceptual accuracy.

Results

On three synthetic scenes with embedded Fe, Ti, and Al implants, the method substantially outperforms all baselines:

Method	Lung	Teeth	Broccoli
FDK	19.04 / 0.924	32.84 / 0.917	11.66 / 0.892
NMAR	20.49 / 0.942	33.05 / 0.923	15.81 / 0.951
Polyner	20.43 / 0.955	30.18 / 0.959	18.88 / 0.987
Ours	29.19 / 0.993	35.97 / 0.992	23.22 / 0.995

(PSNR3D in dB / SSIM3D.) The gains are largest where artifacts are most severe—the Broccoli scene improves by over 4 dB relative to the best baseline—and supervised methods (ACDNet, DICDNet, OSCNet) perform worse than classical baselines here, underscoring their dependence on in-distribution training data. On five real scans from a Bruker SKYSCAN 1273 system (walnut with pins, aluminum-rod phantom, chicken wrapped in wire, bell pepper and broccoli with rivets), qualitative comparisons show sharp structural boundaries and suppressed streaking where FDK, LIMAR/NMAR, Polyner, and Park et al. leave residual artifacts or fail to adapt to cone-beam geometry.

Computationally, the method completes in roughly 16–31 minutes per scene versus 1–2 hours for Polyner and Park et al.—an order-of-magnitude speedup attributable to the explicit Gaussian representation. Relative to the monochromatic R²-Gaussian baseline, per-iteration cost increases slightly, but convergence within 20k iterations (versus ~30k for the baseline) yields comparable or faster wall-clock times on most scenes.

Ablations attribute most of the improvement to the polychromatic attenuation model (+7.05 dB alone over baseline) versus the system response model (+0.53 dB alone), with the combination reaching 29.19 dB. Performance peaks at $N=15$ spectral bins and degrades slightly beyond. Sensitivity analysis on the normalized energy half-range $\gamma$ shows best results when it matches the true spectrum range (90 keV), with degradation of up to 1.37 dB when mismatched—so although the spectrum shape is self-calibrated, the maximum photon energy $r$0 must still be supplied as a known quantity.

Limitations and open questions

The paper concedes several constraints plainly. No clinical CT data were available, so evaluation relies on synthetic human-body phantoms and organic objects with inserted metals; generalization to real clinical acquisitions remains unverified. The physics-inspired assumptions may break down under photon starvation or partial volume effects, and the simplified system response and attenuation models mean reconstructed linear attenuation coefficients can deviate from true physical values for specific materials. The requirement that $r$1 be known in advance is a residual prior not eliminated by self-calibration. Finally, comparisons against Polyner and Park et al. required reimplementation since no CBCT-compatible public code exists, introducing potential reproduction variance despite careful tuning.

Conclusion

This work demonstrates that a compact, physics-grounded polychromatic forward model—two-parameter system response plus a Compton/photoelectric density decomposition—can be integrated into Gaussian Splatting to correct beam hardening in CBCT efficiently and without metal masks or spectral priors. The combination of state-of-the-art accuracy (up to +8.5 dB over the strongest baselines), order-of-magnitude speedups over NeRF-based alternatives, and released artifact-laden datasets makes a concrete case for splat-based reconstruction as a practical alternative to neural field methods in artifact-resilient CBCT.