TR-GS: High-Fidelity Sparse-View CT Volumetric Rendering via t-Distribution Gaussian Splatting and Ray-Confidence Modeling

Zedong Xiao; Yiren Wang; Zhou Liu; Xiaolin Liu; Zhangji Lu

cs.CVAug 17, 2026

TR-GS: High-Fidelity Sparse-View CT Volumetric Rendering via t-Distribution Gaussian Splatting and Ray-Confidence Modeling

Authors: Zedong Xiao, Yiren Wang, Zhou Liu, Xiaolin Liu, Zhangji Lu

Organizations: Shenzhen University Shenzhen, China · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) Shenzhen, China

Abstract

High-fidelity 3D medical visualization supports applications such as clinical assessment and surgical planning. Sparse-view computed tomography (CT) can reduce projection requirements and associated radiation exposure, but limited observations may introduce structural artifacts and reconstruction uncertainty. Although 3D Gaussian Splatting (3DGS) provides an efficient explicit representation for volumetric rendering, existing CT methods based on standard Gaussian primitives may be sensitive to unreliable observations under sparse-view acquisition. We present TR-GS, a Gaussian-splatting framework for sparse view CT volumetric rendering. TR-GS replaces standard Gaussian primitives with projectable Student's t-distribution primitives and introduces a ray-confidence model that regulates their degrees of freedom according to local ray observability. Confidence-guided 3D wavelet regularization is further used to balance high-frequency detail preservation and noise suppression. This work is licensed under a Creative Commons Attribution 4.0 International License. Experiments on synthetic and real-world datasets show that TR-GS improves over representative baselines in most evaluated settings and remains competitive in the remaining cases. The resulting volumetric representations may support downstream medical multimedia applications, including XR-based visualization and interactive clinical rendering.

Figures & tables

Figure 1. Sparse-view CT reconstruction comparison at 18 views. In this example, TR-GS reconstructs clear anatomical structures and obtains a PSNR of 35.30 dB and an SSIM of 0.933. Comparison of sparse-view CT reconstruction results from different methods at 18 views. TR-GS produces clearly visible anatomical structures with reduced artifacts.

Figure 2. Training pipeline of TR-GS. (a) Overall training pipeline: TR-GS replaces Gaussian ellipsoids (thin-tail) with t-distribution ellipsoids (heavy-tail) for robustness. FDK-initialized t-ellipsoids are optimized via three parallel branches: X-ray rasterization for projection rendering, voxelization with wavelet regularization, and ray-confidence modeling. (b) Conceptual ray-confidence pipeline: geometric confidence from ray coverage is used to compute a target degree of freedom (denoted as target_v in the figure, and as $\nu_{i}^{\text{target}}$ in the text), which regularizes the actual $\nu_{i}$ to enhance robustness for poorly-observed primitives. (c) 3D wavelet regularization: local volumetric patches are mapped to ellipsoids and enhanced in the wavelet domain to preserve anatomical details. Training pipeline diagram of TR-GS showing the overall framework with three parallel optimization branches: differentiable X-ray rasterization for projection rendering, density voxelization with wavelet regularization, and ray-confidence modeling for adaptive degree-of-freedom regulation.

Figure 3. $t$ -ellipsoids with varying $\nu$ . As $\nu$ decreases, the ellipsoids exhibit heavier tails (more robust to outliers); as $\nu\to\infty$ , the $t$ distribution converges to Gaussian. Visualization of Student's t ellipsoids under different degrees of freedom. Lower values of nu produce heavier-tailed ellipsoids that are more robust to outliers; as nu approaches infinity, the t distribution converges to a Gaussian shape.

Figure 4. Illustration of ray - confidence modeling. (Left) Geometric reliability: rays intersect the local unit sphere, forming ray support regions of varying thickness; the projected ellipse indicates the detector footprint. (Right) Mapping from confidence score $c_{i}$ to target degree of freedom. Illustration of ray-confidence modeling. Left: geometric reliability diagram showing rays intersecting a local unit sphere around a primitive, forming ray support regions. The projected ellipse on the detector plane is also shown. Right: mapping curve from confidence score to target degree of freedom.

Figure 5. Confidence-guided wavelet regularization. Symbols: $\mathbf{V}$ : local volume block; $\{T_{i}\}$ : set of primitives; green/red neighbors: high - /low - confidence ( $c_{j}\geq\tau$ / $c_{j}<\tau$ ); enhanced primitive (darkened) results from the wavelet loss $\mathcal{L}_{\text{wavelet}}=\lambda_{\text{supp}}S-\lambda_{\text{enh}}E$ (Eq. 15 ); final volume $\mathbf{V}^{\prime}$ . Diagram of confidence-guided wavelet regularization. A local volumetric block is decomposed via 3D discrete wavelet transform. Neighboring primitives are partitioned into high-confidence (green) and low-confidence (red) groups based on a threshold, routing voxels to enhancement or suppression to produce the final enhanced volume.

Synthetic dataset
Methods	12		18		25
Methods	PSNR 3D	SSIM 3D	PSNR 3D	SSIM 3D	PSNR 3D	SSIM 3D
FDK	16.74	0.224	18.78	0.296	20.77	0.371
ASD-POCS	26.10	0.813	27.66	0.856	29.26	0.893
SART	26.06	0.807	27.60	0.849	29.17	0.885
SAX-NeRF	30.21	0.840	32.18	0.886	34.12	0.904

Table 1. Volumetric reconstruction results on the synthetic and real-world datasets under 12, 18, and 25 views. The top three results are highlighted in red, orange, and yellow, respectively. Comparison of volumetric PSNR and SSIM for six reconstruction methods on synthetic and real-world datasets under 12, 18, and 25 views.

Synthetic dataset
Methods	12		18		25
Methods	PSNR 2D	SSIM 2D	PSNR 2D	SSIM 2D	PSNR 2D	SSIM 2D
SAX-NeRF	40.08	0.965	42.46	0.973	45.36	0.980
R 2 -Gaussian	40.14	0.968	43.90	0.978	46.64	0.982
Ours	40.73	0.972	44.54	0.981	47.29	0.984
Real-world dataset

Table 2. Projection-domain results on the synthetic and real-world datasets under 12, 18, and 25 views. The top three results are highlighted in red, orange, and yellow, respectively. Comparison of projection-domain PSNR and SSIM for SAX-NeRF, R2-Gaussian, and TR-GS on synthetic and real-world datasets under 12, 18, and 25 views.

Methods	Low Noise		Medium Noise		High Noise
Methods	PSNR 3D	SSIM 3D	PSNR 3D	SSIM 3D	PSNR 3D	SSIM 3D
Synthetic dataset - 12-view
R 2 -Gaussian	30.73	0.861	30.31	0.843	28.97	0.820
TR-GS	31.03	0.872	30.55	0.857	28.85	0.825
Synthetic dataset - 18-view
R 2 -Gaussian	33.28	0.900	33.04	0.893	29.89	0.828

Table 3. Noise robustness on the synthetic dataset under 12, 18, and 25 views. Low, Medium, and High denote increasing mixed Poisson–Gaussian noise levels. Best results are highlighted in red. Comparison of volumetric PSNR and SSIM for R2-Gaussian and TR-GS under three mixed Poisson–Gaussian noise levels and three sparse-view settings.

6-view
Synthetic	PSNR 3D	SSIM 3D	PSNR 2D	SSIM 2D
Base	26.67	0.798	33.94	0.947
Base + Ray-confidence model	26.73	0.803	33.97	0.946
Base + 3D wavelet regularization	26.68	0.798	33.96	0.947
Full	26.70	0.805	33.99	0.949

Table 4. Core-module ablation on the synthetic dataset under 6, 12, 18, 25, and 50 views. Best results are highlighted in red. Ablation results for the Student's t base model, ray-confidence model, confidence-guided wavelet regularization, and full TR-GS model under five view settings.

$T$	Spearman $\rho$	PSNR 3D $\uparrow$	SSIM 3D $\uparrow$	PSNR 2D $\uparrow$	SSIM 2D $\uparrow$
0.10	0.87	30.90	0.870	40.79	0.972
0.25	0.66	31.05	0.874	40.79	0.974
0.50	0.56	30.96	0.867	40.75	0.973

Table 5. Sensitivity of the ray-confidence temperature

T

on the synthetic 12-view setting. Sensitivity analysis of the temperature parameter in the ray-confidence model, showing Spearman rank correlation between learned degrees of freedom and confidence scores, along with reconstruction metrics.

Figure 6. Colorized slice examples of different methods, with PSNR (dB) shown at the bottom right of each image. In the shown examples, TR-GS recovers finer anatomical structures and exhibits fewer streak artifacts than the compared methods, particularly at 12 and 18 views. Colorized CT slice comparison across different reconstruction methods including FDK, ASD-POCS, SART, SAX-NeRF, R2-Gaussian, and our TR-GS method. PSNR values are shown at the bottom right of each slice image. In the shown examples, TR-GS recovers finer anatomical structures with reduced streak artifacts.

Method	Density Control	Optimizer	PSNR 3D (dB)	SSIM 3D
R 2 -Gaussian	ADC	Adam	33.28	0.900
	AR	Adam	32.44	0.891
	AR	SGHMC	32.47	0.892
	ADC	SGHMC	32.41	0.891
TR-GS (Ours)	AR	SGHMC	33.66	0.907
	AR	Adam	33.45	0.904

Table 6. Optimizer and density-control ablation under the 18-view low-noise setting. Best results within each method are highlighted in red. Comparison of Adam and SGHMC optimizers with ADC and AR density-control strategies for R2-Gaussian and TR-GS.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Synthetic, 12-view
$\tau$	PSNR 3D $\uparrow$	SSIM 3D $\uparrow$	PSNR 2D $\uparrow$	SSIM 2D $\uparrow$
0.10	30.95	0.870	40.74	0.968
0.35	31.05 $\checkmark$	0.874 $\checkmark$	40.79 $\checkmark$	0.974 $\checkmark$
0.50	30.99	0.870	40.78	0.972
0.80	30.94	0.866	40.65	0.969

Appendix

Table 7. Sensitivity to the confidence threshold

\tau

in the confidence-guided wavelet regularization.

Synthetic, 12-view
Enhancement factor	PSNR 3D $\uparrow$	SSIM 3D $\uparrow$	PSNR 2D $\uparrow$	SSIM 2D $\uparrow$
1.50	31.05 $\checkmark$	0.874 $\checkmark$	40.79 $\checkmark$	0.974 $\checkmark$
2.00	31.03	0.873	40.78	0.972
4.00	31.02	0.870	40.71	0.972
8.00	30.96	0.870	40.69	0.968

Appendix

Table 8. Sensitivity to the enhancement strength in the confidence-guided wavelet module.

Figure 7. Reconstruction results on the synthetic dataset.

Figure 8. Reconstruction results on the real-world dataset.

Explore similar work

Residual Gaussian Splatting for Ultra Sparse-View CBCT Reconstruction
Apr 30, 2026Jian Lin, Jiancheng Fang, Shaoyu Wang +43D Gaussian Splatting Cone-Beam CT
School of Information Engineering, Nanchang University, Nanchang 330031, China · Laboratory of Image Science and Technology, the School of Computer Science and Engineering, and the Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, Southeast University, Nanjing 210096, China
TurboGS: Accelerating 3D Gaussian Splatting via Error-Guided Sparse Pixel Sampling and Optimization
Jun 14, 2026Zheng Dong, Daifei Qiu, Pinxuan Dai +53D Gaussian Splatting 3DGS Acceleration
Zhejiang Sci-Tech University · Malanshan Audio&Video Laboratory · CAD&CG Laboratory, Zhejiang University +2
Projection-Volume Fidelity Divergence: Diagnosing and Controlling Optimization Drift in Sparse-View 3D Gaussian Tomography
Jun 21, 2026Yikuang Yuluo, Ao Wang, Shen Kuan +63D Gaussian Splatting Adaptive Gaussian Densification
1Chongqing University, Chongqing, China · 2Peking University Health Science Center, Beijing, China

Apr 30, 2026J/K move · Enter open · S save

Residual Gaussian Splatting for Ultra Sparse-View CBCT Reconstruction

Jian Lin, Jiancheng Fang, Shaoyu Wang, Changan Lai+3

School of Information Engineering, Nanchang University, Nanchang 330031, China · Laboratory of Image Science and Technology, the School of Computer Science and Engineering, and the Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, Southeast University, Nanjing 210096, China

3D Gaussian Splatting Cone-Beam CT Sparse-View CT Reconstruction

Open paper AskPDF arXiv

While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view conditions, leading to over-smoothing and a loss of high-frequency anatomical details. Since wavelet transforms provide rich high-frequency information and have been widely utilized to enhance sparse reconstruction, this work integrates wavelet multi-resolution analysis with 3DGS. To circumvent the mathematical mismatch between the strict non-negativity of physical X-ray attenuation and the bipolar nature of high-frequency wavelet coefficients, we propose Residual Gaussian Splatting (RGS). Methodologically, we introduce a spectrally-decoupled Gaussian representation that stratifies the volumetric field into a geometric base component and a residual detail component. This decomposition systematically transforms explicit high-frequency fitting into a physically consistent, implicit residual compensation task. Furthermore, we devise a spectral-spatial collaborative optimization strategy to coordinate the interplay between geometric anchoring and texture refinement, effectively preventing spectral crosstalk. Extensive experiments on clinical datasets demonstrate that RGS enables the reconstructed images to capture highly refined geometric textures. It successfully resolves the trade-off between artifact suppression and detail preservation, yielding superior visual fidelity in complex trabecular and vascular structures compared to existing neural rendering baselines.

Abstract

Explore similar work

Residual Gaussian Splatting for Ultra Sparse-View CBCT Reconstruction

TurboGS: Accelerating 3D Gaussian Splatting via Error-Guided Sparse Pixel Sampling and Optimization

Projection-Volume Fidelity Divergence: Diagnosing and Controlling Optimization Drift in Sparse-View 3D Gaussian Tomography